The wet conditions made life difficult but Peter Halmosi and Paul Connolly went close for Argyle early on, while Jamie McCombe went close for City.
Sylvan Ebanks-Blake's penalty gave Plymouth the lead on 23 minutes after Louis Carey's foul inside the box.
Lee Trundle's arrival gave the visitors more of an edge, and they were rewarded when Timar headed into his own net.
Plymouth manager Paul Sturrock:
"We looked tired in the second half and I feel four games in 10 days for a small number of players has had a draining effect.
"The pleasing thing was that we did not cave in after we gave away an own goal for them to equalise."
Bristol City manager Gary Johnson:
"Alot of fans attended today and it would have been a shame to have it called off, so I'm glad it went ahead.
"We had some good chances, with Lee Trundle twice forcing saves from the man-of-the-match - their goalkeeper. But Plymouth had chances too."
Plymouth: Larrieu, Connolly, Timar, Seip, Hodges, Norris, Abdou, Nalis, Halmosi, Easter (Fallon 77), Ebanks-Blake (Chadwick 75).
Subs Not Used: McCormick, Doumbe, Gosling.
Booked: Nalis, Connolly.
Goals: Ebanks-Blake 23 pen.
Bristol City: Basso, Orr, Carey, McCombe, Fontaine, Sproule (Skuse 85), Elliott, Johnson, McIndoe, Noble (Trundle 46), Showunmi (Byfield 67).
Subs Not Used: Weale, McAllister.
Goals: Timar 71 og.
Att: 16,530
Ref: Phil Dowd (Staffordshire).
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