Arsenal struggled to break down Hull following the 45th-minute dismissal of George Boateng - but Bendtner earned a fifth straight win by netting after Denilson's swerving shot was tamely parried by Boaz Myhill.
Arsenal were far from their fluid best - illustrated in the 5-0 Champions League win over Porto in midweek - but Hull must be given credit for disrupting the visitors' rhythm and were ultimately unlucky to suffer a fourth straight loss.
The Tigers remain in the relegation zone with nine games remaining.
Bullard was retained in the starting XI and Nick Barmby dropped to the bench in one of six changes made by manager Phil Brown in the wake of the 5-1 humiliation at Everton.
The two City midfielders were this week involved in an altercation in front of members of the Women's Institute near the Humber Bridge.
Captain Cesc Fabregas was still absent for the Gunners and his playmaking ability was missed.
Jozy Altidore flashed a right-footed shot from 20 yards wide after turning Campbell early on before Vennegoor of Hesselink nearly got on the end of Bullard's chip forward.
The burly City forward pairing were clearly drafted in to get physical with Campbell and Thomas Vermaelen from the start, but Arsenal's defensive duo stood firm and the visitors pounced on the break after 14 minutes.
Having scored three in the 5-0 midweek win, it was no surprise to see Bendtner involved in the opener.
The Dane found Arshavin with a pass across the edge of the box and the Russian stumbled through attempted tackles from Boateng and Bernard Mendy before prodding beyond Myhill.
Hull equalised from the spot after Campbell was adjudged to have hauled down Vennegoor of Hesselink.
Dean Marney's ball was flicked on by Craig Fagan to the Dutchman, who appeared to be in an offside position, but Campbell's attempted tackle led referee Andre Marriner to point to the spot.
Bullard stepped up and converted into the top corner.
Campbell was booked and City's Andy Dawson followed for a late tackle on Denilson.
Boateng and Bendtner were yellow carded for an exchange in the aftermath of the foul in scenes reminiscent of a fracas which saw the teams fined following their last meeting in December.
Gael Clichy forged forward down the left and went down in the area under a challenge of Boateng, but found himself booked retrospectively for a dive in a frantic final few moments of the first half.
And Boateng was soon walking off prematurely after a high challenge on Sagna saw the Hull captain dismissed for a second yellow.
The numerical disadvantage forced Brown into a reshuffle, with Altidore moving wide and Vennegoor of Hesselink going it alone up front.
But in a scrappy opening to the second half, Kamil Zayatte was fouled by Campbell and had to go off moments later.
Arsenal encountered stern resistance and Bullard attempted to relieve the pressure for 10-man Hull only to see his 25-yard drive go over.
Arsene Wenger introduced Theo Walcott and the England international's pace had an immediate impact.
He soared through on the right, cut back for Samir Nasri and Arshavin ballooned the ball over.
Arshavin and Walcott combined to gift Bendtner an opportunity, but the striker's poor effort was blocked and looped out for a corner.
Walcott then had a half chance from Arshavin's pull back but could not connect.
Altidore was withdrawn for Kevin Kilbane late on and Hull put men behind the ball to frustrate Arsenal.
There were six minutes of stoppage time and the visitors threw men forward.
Clichy had a shot from wide on the left, but Myhill was fully behind it.
The Tigers stopper could only block a swerving effort from Denilson soon after, but Bendtner reacted first to break the hosts' resistance and earn the Gunners a valuable win.