Elgin keeper Kieron Renton put up the shutters as the league leaders failed to turn dominance into goals.
East Fife started 23 points ahead of lowly City and were almost ahead on three minutes when Renton's clearance cannoned off Craig Smart, but held up in the wind and was cleared.
Neil Jablonski forced Renton to block with his feet on 11 minutes and Ryan Blackadder hit a 20 yarder just wide as the Fifers swarmed towards their goal.
But, in a rare counter-attack Adam Moffat sent a pane free-header into John Dodds' gloves and they were made to pay on 33 minutes.
Renton somehow kept out Tom Courts header but was powerless to stop Sam Linton netting the rebound.
To their credit Elgin forced the Fifers back and Martin Johnston was centimetres away from Craig Campbell's cross on 52 minutes.
City grabbed a deserved equaliser on 62 minutes when Dodds dropped a free kick and Paul Kaczan rifled the loose ball into the net.
Dave Baikie threw on veteran Scott Crabbe for Craig O'Reilly and the striker was almost a hero but his shot on the turn bounced wide.
Renton made sure City got a point when he made two great saves from Blackadder and Crabbe.