Padraig Amond had given Stanley a 74th-minute lead against the run of play, tapping home Will Hatfield's right-wing cross.
Connell had only been on the pitch six minutes when he got on the end of James Hanson's flick in the 83rd minute and looped the ball over goalkeeper Ian Dunbavin from 12 yards for his first City goal following his summer move from Swindon.
Bradford should have led at the break after dominating the first half. Zavon Hines had a fierce strike punched out by Dunbavin before the forward latched onto a long pass from James Hanson and was clean through but hit the far post from 12 yards out after 16 minutes. Hines returned the favour by setting up Hanson but his looping header was cleared off the line by Luke Joyce.
Accrington could not get going as an attacking force and were lucky to go in goalless at the interval. After the break it was more of the same with Bradford pressing but Stanley came more into it with Romuald Boco, on his second home debut for the club, and Joyce both firing narrowly off target.
Amond then made one count and the hosts had to soak up the pressure with Connell sending a close-range effort into the hands of Dunbavin. Connell then got the goal to make it a lively finish as both sides chalked up a League Two draw for the first time this season.