The Bantams, who have now gone seven league and cup games at home without a win, looked set to end that dismal run, but after taking a two-goal lead they let the Gulls back into the game in sloppy fashion.
Bradford's new striker Andy Cooke marked his home debut with a 33rd minute strike and, when top-scorer Dean Windass added a second two minutes later, Colin Todd's promotion hopefuls should have wrapped up the win.
But a Tony Bedeau header gave the Gulls a lifeline and a ricochet off Akinfenwa saw them draw level before the break.
Torquay, who had only won one of their last 10 games, made a bright start at a ground where they had not won since 1972 and City had a let-off after 16 minutes when winger Jo Kuffour blazed wide with only the keeper to beat.
The two sides had fought out a grim 0-0 draw last month and there was little sign of the goal frenzy to come as City failed to breakdown the visitors determined defence.
But when Nicky Summerbee's free-kick fell kindly for Cooke the striker wasted no time in turning neatly 14 yards out and firing a low right drive passed Olafur Gottskalksson.
Two minutes later Summerbee was provider again this time picking out Cooke with a cross to the far post and, when his header rebounded off the keeper's chest, Windass was on the spot to head the loose ball home from inside the six yard box.
The home fans were still celebrating when the Gulls struck back after 40 minutes thanks to Akinfenwa's strength in the air.
The impressive front man out-jumped his marker only for his header to rattle the City bar, but when the ball came back into play, midfielder Bedeau headed home the rebound.
Things went from bad to worse for City two minutes later when Gulls' skipper Craig Taylor headed goalwards and, although David Wetherall headed his effort off the line, his team-mates failed to clear the danger.
Full-back Darren Holloway reacted first, but when his attempted clearance struck the unsuspecting Akinfenwa the ball rebounded off his body and flew agonisingly into the City net.
After a frantic finish to the first half there was little to cheer after the break and City were lucky to survive a penalty shout when Kuffour seemed to be tugged by substitute full-back Peter Atherton.
Referee Mark Cowburn waved away the appeals and the Gulls would have felt aggrieved had keeper Gottskalksson not pushed Ben Muirhead's late drive wide.