Bath duo Francois Louw and Matt Banahan and Leicester's Brett Deacon were all shown red cards for foul play between the 60th and 65th minutes.
The dismissals proved a turning point in the game because Bath, who had just lost Simon Taylor to the sin-bin, saw their 12-6 lead - gained through tries from Stephen Donald and Tom Biggs - eroded as the hosts scored 11 points in five minutes.
Adam Thompstone crossed for Leicester's try, with the rest of the Tigers' points coming from the boot of George Ford.
It was a much-needed win for Leicester after last week's defeat at Wasps, while Bath, who beat leaders Harlequins last week, will be kicking themselves for their indiscipline.
Both teams were boosted by the return of some of their internationals, Leicester able to recall props Marcos Ayerza and Martin Castrogiovanni, with Horacio Agulla, Paul James and Louw back for Bath.
It was an emotional return to Welford Road for Argentina back Agulla, who joined Bath last summer, and there was added spice to the match for Leicester fly-half George Ford, whose father Mike is the Bath defence coach.
Last season Ford got the better of his father, who was then at Newcastle, in a one-sided game, but Bath were a much tougher proposition and they led 5-0 at half-time thanks to a fine solo try from their New Zealand fly-half Donald.
They were good value for it, too, for they ran hard and were adventurous when attacking and defended resolutely in their own 22.
Leicester created chances but were far too wasteful and Ford turned down several kickable penalties after missing attempts in the ninth and 15th minutes.
Donald missed a long-range penalty in the third minute and then Bath threw everything but the kitchen sink at Leicester, whose defence was rock solid.
But Bath drew first blood in the 13th minute after a fine break by full-back Nick Abendanon. From the ruck, Donald threw a couple of dummies before running straight over full-back Mathew Tait for a terrific try, which he failed to convert.
Ford missed penalties either side of the Bath try before putting Leicester in a great attacking position with a fine touch kick, but they wasted the chance with the referee penalising them for crossing when surging to the line from the line-out.
They passed up another chance to score from a line-out two minutes later and their lack of precision told again when they had a try chalked off for a forward pass.
It came after a brilliant counter-attack which twice involved Tait and winger Thompstone down the left, and when Leicester switched the attack to the right lock Graham Kitchener put Niall Morris over with a long floated pass only to see the video referee adjudge it to have gone forward.
After last week's defeat at Wasps, Leicester boss Richard Cockerill slammed his side, saying not one player deserved to wear the shirt. He demanded an improvement and, while there was commitment in spades, Leicester paid the price for poor basic skills, another chance going begging in the 34th minute when Anthony Allen threw a long pass to Thompstone that ended up in touch.
Whatever the Leicester coaches said at the break had an effect because they started the second half at a gallop and, when they won a penalty 40 metres out, Ford made no mistake.
Bath found themselves down to 14 men when number eight Taylor was sin-binned for obstruction on Tait in the 50th minute, and five minutes later Ford put Leicester ahead for the first time at 6-5 with a tremendous penalty from 46 metres.
The lead, however, lasted just two minutes because Bath hit back with their second try, winger Biggs cantering over after great work by Donald and Banahan.
Donald added the conversion to put Bath 12-6 ahead but there was another twist moments later when Bath flanker Louw was sent off for use of the elbow.
Leicester took advantage immediately, Thompstone scoring after Leicester had driven to the line from a line-out. Ford missed the conversion.
Worse followed when Michael Claassens conceded a needless penalty, pushing Allen in the back during a Leicester counter-attack and allowing Ford to kick an easy penalty.
And then Banahan was also sent off for a high tackle on Allen. Allen was left prostrate on the ground for several minutes while the medics attended to him before being carried off on a stretcher.
Leicester flanker Deacon was also sent off after the incident for appearing to throw a punch.
The madness continued when Donald was sin-binned for also appearing to throw a punch, before Ford put Leicester 17-12 up with his fourth penalty 12 minutes from time.
London Welsh claimed a 15-9 victory over basement rivals London Irish at the Kassam Stadium.
However the game was ruined as a contest by the early dismissal of number eight Chris Hala'ufia which resulted in the visitors having to play 70 minutes with 14 men.
The match was a dreadful spectacle with neither side having any attacking invention to break down the opposition's defence and it was left to Gordon Ross to secure victory for his side with five penalty goals.
London Welsh took a fifth-minute lead when Ross kicked his first penalty after Irish were penalised for dragging down a lineout drive.
Almost immediately, Welsh suffered a big blow when influential centre Hudson Tonga'uiha left the field with what appeared to be a serious shoulder injury.
Irish had their first opportunity for points but Ian Humphreys was narrowly short with his 45-metre penalty attempt.
The visitors then suffered a huge set back when Hala'ufia was sent off for a dangerous tip tackle on Welsh replacement Seb Jewell. The referee JP Doyle sought the advice of his touch judge before issuing a red card.
Hala'ufia expressed his regret by immediately walking over to the uninjured Jewell to shake his hand but the damage was already done.
The resulting penalty was kicked by Ross.
With 15 minutes gone, Irish were again penalised to enable Ross to kick his third penalty to give his side a handy 9-0 advantage.
Tom Homer put Irish on the scoreboard with a penalty before the visitors were given further hope when Humphreys kicked another.
When Matt Garvey carelessly lost possession, Irish again offended for Ross to be on target.
With two minutes of the half remaining, Homer had the opportunity to reduce the arrears but his kick from just inside his own half sailed narrowly wide to leave Welsh deservedly ahead 12-6 at the interval.
Irish introduced Halani Aulika at prop for the second half and were unlucky not to get the first points of the half when Humphrey's penalty rebounded back off a post.
The visitors' woes continued when flanker Garvey was sent to the sin bin for a deliberate offside before Humphreys again missed with another penalty attempt.
Playing against 13 men, Welsh blew their best chance. Tom Arscott neatly chipped through for Nick Scott to run on to.
The wing was first to the ball and booted it over the try line but somehow Tyson Keates failed to secure the easy touchdown.
Garvey returned with no damage to the score line but once again Irish offended at the line out to allow a kick from Ross to scrape over via the crossbar.
Homer missed with a long range penalty but fifteen minutes from time succeeded with another as the spirited Irish raised their game.
When Sonny Parker was yellow carded for a deliberate offside with 10 minutes to go, Irish scented an unlikely win but Welsh hung on.
Exeter remain unbeaten at Sandy Park this season as they moved up to fifth place in the Aviva Premiership table with a 30-23 win over Wasps.
The scores were level at 20-20 at half-time, with both sides scoring two tries in the second quarter - the visitors' second coming from a blatant forward pass which questions why TMOs are not at every Premiership match.
Both sides battled and were battered after the break with the Chiefs scoring a converted try and a penalty, while Wasps secured a losing bonus point with a penalty from replacement Tommy Bell just before the final whistle.
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