Warriors' first victory over the Tigers since March 2006 looked likely for large parts of a gripping encounter.
But Leicester prevailed, courtesy of two second-half penalty tries, the second one being awarded in the final minute by referee JP Doyle.
Worcester wing David Lemi scored an early try and three Andy Goode penalties against his former club ensured Warriors occupied the driving seat.
Leicester, though, mounted a fightback either side of Goode being sin-binned, with wing Scott Hamilton touching down before Tigers claimed an opening penalty try that England international Toby Flood converted.
Flood also missed three penalties, but he added the extras to Tigers' late clincher and Worcester were denied as Leicester went top above long-time league leaders Harlequins.
And their night was made doubly sweet by England flanker Tom Croft making an impressive 50-minute contribution on his first appearance since suffering a neck injury last April.
Croft's return was among 12 changes to the Leicester side that accounted for Gloucester last weekend, with England trio Manu Tuilagi, Tom Youngs and Geoff Parling all rested from a team captained by lock Louis Deacon.
Worcester boss Richard Hill, meanwhile, made six switches following the defeat against Premiership relegation favourites Sale Sharks last time out, including a start for scrum-half Jonny Arr instead of jaw injury victim Paul Hodgson.
England head coach Stuart Lancaster was among a capacity Sixways crowd of just over 12,000, and Worcester made all the running as they established an 8-0 lead inside the opening 16 minutes.
Goode landed a penalty when Tigers infringed in front of the posts 35 metres out, then slick work by centre Jon Clarke and full-back Chris Pennell created Lemi's fifth Premiership try this season.
Leicester were rocked back on their heels, unable to establish a territorial foothold, and Goode extended Worcester's advantage through another penalty when Tigers prop Martin Castrogiovanni infringed.
There was no stopping Worcester, with Goode completing his penalty hat-trick shortly after Castrogiovanni was yellow-carded by Doyle for an illegal tackle.
Leicester, despite fielding 10 internationals, had no answer to Worcester's accuracy and verve, with Warriors retaining a vice-like grip on the contest as half-time approached.
Wing Josh Drauniniu had a couple of chances to test the Leicester defence, but Tigers gave themselves a lifeline deep into injury time.
Flood and full-back Mathew Tait combined to send Hamilton over in the corner, yet there was more grief for Worcester when Goode became Warriors' 11th Premiership sin-binning this season for dropping his knee on the New Zealander as he touched down.
It was dreadful indiscipline by Goode, but Flood missed the conversion and then a penalty from halfway, and Worcester trooped off 14-5 ahead.
With Goode still off, Pennell took over goalkicking duties, but he missed two chances in as many minutes before Goode returned.
Leicester, though, now had momentum, and with international props Dan Cole and Marcos Ayerza appearing off the bench, there was no let-up for Worcester as Doyle punished them for collapsing a scrum by awarding Tigers a penalty try.
Flood slotted the conversion, which cut Worcester's advantage to just two points, but Warriors regained their composure with Goode once again pulling the strings.
Despite Goode missing a 67th-minute penalty, Worcester were again asking Leicester questions, and the visitors needed to regroup as they targeted a sixth successive victory in all competitions.
Leicester laid siege inside Worcester's 22 as the clock ticked down, and their pressure was rewarded with another penalty try when Warriors' scrum capitulated.
Tigers then had a mere 10 seconds to hold on from the restart, and Worcester - not for the first time this season - were left to fret about a game that got away.
- Sports & Recreation
- Andy Goode