After Argyle took the lead midway through the first half through Sylvan Ebanks-Blake's eighth Championship goal of the season, they came under intense pressure from their visitors.
Thanks to a marvellous display of goalkeeping by man-of-the-match Romain Larrieu, the Pilgrims looked like hanging on for all three points.
However, the Frenchman was eventually beaten by a freak own goal from his own centre-back Krizstian Timar, who turned Liam Fontaine's innocuous cross into his own net.
Referee Phil Dowd took 25 minutes before passing the Home Park pitch fit for the game, but the pre-match soaking was nothing compared to the storm Argyle had to weather for most of the match.
They took the lead after 23 minutes when Ebanks-Blake was pulled back by City skipper Louis Carey after David Norris had played him in.
Carey was clumsy rather than malicious, but Ebanks-Blake converted the penalty opportunity, sending the ball into the corner and just out of the reach of Brazilian goalkeeper Adriano Basso.
City introduced Lee Trundle from the substitute's bench at half-time and, supported by wide men Ivan Sproule and Michael McIndoe, he made a difference.
He set up Marvin Elliott for a shot which the midfielder fired wastefully over, then pulled out a full-stretch save from Larrieu who blocked Sproule's follow-up.
Apart from a snap-shot by Ebanks-Blake that Basso clawed away, the second half was virtually all Bristol.
They were rewarded for their endeavour when Timar put through his own net after mis-kicking Fontaine's delivery and slicing a high ball over Larrieu's head.
Larrieu beat out another shot on the turn from Trundle and then similarly denied substitute Darren Byfield as Argyle held on for a point.