Stuart McCall recovered from a stiff back to lead City against his old club at Goodison and Wayne Jacobs passed a fitness test on his tweaked hamstring.
But Jim Jefferies was forced to make his first change for three matches after midfielder Gareth Whalley failed to shake off the stomach bug that has been going round the club in the last fortnight.
His place was taken by Jamie Lawrence who had been restricted to only two starts since Christmas because of injuries. But he came through Jamaica's World Cup qualifier against Honduras in midweek.
Everton welcomed back fit-again quartet Steve Watson, Richard Gough, David Unsworth and Duncan Ferguson. But there was no Paul Gascoigne - or African runaway Alex Nyarko.
Again the relegation equation for City was simple. Anything less than a win and the Bantams were down - and they had only won once in the league at Everton 92 years ago.
City made a sensational start when they roared into the lead after only two minutes.
Robbie Blake forced a corner and from Benito Carbone's left-wing kick, Andy MYERS got above Watson to bury a header into the Everton net.
It was the defender's first goal of the season and sent the small section of away fans wild.
But Everton would have been back on terms in the ninth minute but for a wonderful one-handed save by Gary Walsh.
Niclas Alexandersson chased a lost cause on the right touchline to keep the ball in play, laying it back to Watson whose cross picked out Kevin Campbell unmarked six yards out. It wasn't the best of headers but Walsh still had to react like a flash to paw it away with his right hand.
David Unsworth was booked after 13 minutes for straight-arming Gunnar Halle as he went up for a header. Robert Molenaar headed Carbone's angled free-kick back to the edge of the penalty area where Blake and Eoin Jess had shots charged down.
Walsh again came to City's rescue when Duncan Ferguson shot on the turn after getting free of his marker Molenaar, the keeper palming the ball over the bar.
Everton's defence looked uncertain at set-pieces and another Carbone free-kick caused unrest in the home ranks. Ferguson whacked the ball away and then turned to berate his back four.
Steve Watson gave Paul Gerrard a lofted back pass to worry about midway through the half. The home goalkeeper chested it down and then just managed to clear as Ward closed in.
Gerrard was then forced into a more orthodox save to clutch a swerving 25-yarder from Carbone.
Michael Ball was trying to get forward for Everton and was rewarded with a lucky bounce off Myers to have a go in the 26th minute but snatched at the ball and blazed over.
Robert Molenaar tested Paul Durkin's patience once too often when he clattered Ferguson on the edge of the area and the Dutchman got a yellow card. Unsworth's free-kick deflected harmlessly off Lawrence.
Jess wasted the chance to break with an under-hit pass aimed for Lawrence and Everton came right back through Campbell who would have picked out Ferguson in front of goal but for a great tackle by Jacobs.
But City should have been two up in the 31st minute. Jess again found plenty of room on the counter and he fed Blake midway inside Everton territory.
He weaved his way into the penalty area but with only the advancing Gerrard to beat, Blake slid his shot a couple of yards wide. It was a big miss and you wondered how critical it could prove to be.
Jacobs appeared to twist his knee as he went into a tackle on Alexandersson. Molenaar handled the Swede's cross but had been pushed in the back by Ferguson. City's left back was able to resume after treatment.
Ward, who had been sailing close to the wind, picked up City's second booking four minutes before half-time after a late tackle on Scott Gemmill.
Halle was caught dithering by Campbell but Lawrence whipped the ball off Gough's toes to concede a throw level with the Bantams box. Gough had a swing at it, missed altogether, but the ball fell nicely for Alexandersson who drilled wide.
Walsh saved low from Ferguson's fierce cross shot but Everton couldn't turn their pressure into goals as City continued to hold firm.
HT: Everton 0 City 1
Everton boss Walter Smith made two changes for the second half with Thomas Gravesen and Tony Hibbert replacing Gough and Unsworth.
And within a minute of the restart the home side were level after some questionable marking.
Ball's throw-in was back-headed across goal by Campbell and FERGUSON nipped round the blind side to fire through Walsh's legs from five yards.
It was the worst possible start to the half for City and it needed a frantic block in front of goal from McCall to deny Ferguson another seconds later.
But City were handed the chance to regain the lead after 55 minutes with a penalty.
Watson was caught dawdling in possession by Carbone and when the Italian fell under his attempt to recover, referee Durkin pointed straight to the spot.
Blake had scored with his previous two spot-kicks in recent weeks - but this time his low effort to Gerrard's right was well saved by the keeper.
Molenaar was punished for a foul on Ball 30 yards out but Watson's free-kick flew into the stand.
But the reprieve was short-lived as Everton went 2-1 up after 65 minutes. Ball's cross was partially cleared by Molenaar as far as ALEXANDERSSON beyond the far post and he swept the ball home.
Yet the topsy-turvy second half immediately took another twist when City were awarded another penalty as Watson handled a shot from Myers.
This time Carbone stepped up to take it - and whipped it several feet over the crossbar.
A deep cross from Halle nearly embarrassed Gerrard who pushed it away for a corner and as City upped the tempo, Ward headed wide.
Campbell almost put the contest out of reach with a stretching shot that brushed Walsh's right post.
And the keeper pulled off another fine save to bat out Campbell's diving header with 13 minutes to go before denying Ferguson with a sharp block low to his right.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article