Kane Hester’s first-half double had given Elgin a two-goal advantage before Allan Smith’s 56th minute header halved City’s arrears.
Scott Shepherd then drilled home an equaliser for City before Blair Henderson, pictured, pounced to net what appeared to be a sensational winner for the visitors with two minutes remaining.
However, in the dying seconds Stephen Bronsky’s measured finish snatched a point for Elgin.
Peterhead slipped to second spot following a sobering 3-0 reverse at fourth-placed Annan Athletic.
David Wilson drove forward to fire Annan into a 53rd-minute lead via the post. Scott Hooper then knocked the ball down for Tommy Muir to double Annan’s advantage on the hour mark, and Muir soon netted his second of the afternoon to seal the win.
Third-placed Clyde capitalised as their 1-0 victory over Cowdenbeath puts them to within two points of Peterhead and three of leaders City.
Ray Grant’s close-range strike midway through the second period propelled the Bully Wee into genuine title contention.
Queen’s Park’s two-and-a-half-month wait for a league win ended in emphatic style as the Spiders demolished second-bottom Berwick Rangers 7-1 at Hampden.
Scott McLean’s 15th-minute penalty and a Kurtis Roberts double had Queen’s Park firmly in control before Berwick’s Kyle Allison was sent off on half-time.
The second half saw David Galt net twice, McLean add his second and Lewis Hawke was also on target before Jordan Orru notched the scantest of consolations.
Bottom side Albion Rovers lost 5-0 at home to Stirling Albion.
Rovers had Declan Byrne dismissed early before a Peter MacDonald’s hat-trick, and further efforts from Darren Smith and Dylan Mackin sealed the points.