Ulsterman Irwin took over the lead of the championship after clinching a double on the BeerMonster Ducati at the Cheshire circuit, winning the Sprint race on Saturday following a dramatic final lap, when team-mate Bridewell made a mistake on the brakes into the chicane and dropped from second to fourth.
In a controversial second race, Bridewell crossed the line first ahead of Irwin but was hit with a Long Lap penalty equivalent of three seconds for unsafe conduct.
The Wiltshire man slowed dramatically and backed up Irwin and the rest of the pack behind the Safety Car at Lodge, almost causing a collision.
He went on to take the chequered flag narrowly ahead of Irwin, but was demoted to sixth in the results when the penalty was applied.
Lee Jackson (Cheshire Mouldings Kawasaki) was second ahead of Kyle Ryde (OMG Yamaha), Leon Haslam (ROKiT BMW) and Josh Brookes (FHO Racing BMW).
Bridewell, who started from pole, was fired up for the final race of the weekend and was able to pull a gap over Irwin on the final three laps, edging ahead to secure his eighth victory of the season by 1.147s, with Jackson just under a second further back in third.
With two rounds of the Showdown remaining, Irwin holds sway at the summit but only by half-a-point as the championship fight heats up.
The 33-year-old Carrickfergus man, who was wearing a special edition helmet as a tribute to team owner Paul Bird – who passed away aged 56 two weeks ago – reflected on an ‘amazing weekend’ at round nine.
“I never thought we’d come away leading the championship at what is Tommy’s strongest track,” said Irwin.
“It’s been an amazing weekend, one that has worked really well with the team.
“Hats off to Tommy, his last three laps were really focused. I had quite a big wheelie between the two chicanes one lap and I couldn’t recover, I was trying and trying, but he deserved the win because he was faultless.”
Race winner Bridewell said the gloves were off going into the final races of an enthralling championship, claiming there was now a ‘divide’ within the team.
In a TV interview after race two, Northern Ireland man Irwin spoke of having ‘common sense’, which he credited to his upbringing, as he discussed the Safety Car incident.
"Growing up with great parents and family upbringing, you have some common sense,” Irwin said. “I thought after the incident [with the Safety Car] ‘I have to be leading this race… surely there’s a penalty’ and obviously it was announced after I came through.”
Irwin later said that he was not making a comparison between his family and Bridewell’s, claiming his words had been ‘misunderstood’.
Following his victory, Bridewell said: “It’s always nice to get the double here at Oulton Park, and nice to get the win for Paul [Bird]. I like to do my talking on the track, Glenn seems to do it both [on and off track].
“I keep my head down, keep my mouth shut and get the job done.
“I’ve got an amazing package around me and an amazing support team, and it’s great.
“There is a divide in the team now – there’s no hiding that – and it’s all-out war.”
Haslam finished fourth ahead of Brookes and Ryde, who is now 60.5 points behind Bridewell in the standings.
Michael Dunlop, riding the Crendon Honda by Hawk Racing, was 19th on Saturday but crashed out of race two. Dunlop had a DNF in the third race.
Round 10 at Donington Park National takes place September 29 to October 1.