The home side started the brighter and it took them only three minutes to test the Rovers back four. Martin Johnston broke through the defence but his lob sailed high over the bar and failed to trouble Jamie Ewings in the Albion goal.
Albion Rovers first chance of the match fell on the 15th minute after Jamie Mckenzie brought down Craig Young on the edge of the box, but Graham McGhee's powerful effort was fired straight into the wall.
The lively Johnston caused Albion problems all afternoon, and the big striker was close to give Elgin the lead but he dragged his shot wide from 12 yards.
Elgin started the second half brightly and Johnston had two good chances inside two minutes but he failed to convert. However it was the visitors who took the lead in the 54th minute when Steven Donachy skinned two Elgin defenders before his lightning strike flew in to the top corner of Elgin's goal.
Elgin were refusing to lie down, and in the 70th minute a high cross from Alan Muir found the head of Johnston but his effort failed to find the target.
Five minutes later Elgin's hard work paid off when 17-year-old subtitute Gary Wood collected the ball on the edge of the area to drill home into the bottom corner.
Elgin will find themseleves hard done bywhen, in the 82nd minute, Paul Kaczan rose to head home only for it to be disallowed by linesman Jeff Banks.
With three minutes left on the clock and Elgin pushing for a win, they were caught on the break by a quick-passing Albion move. The ball eventually fell to George Wallace, who shot home powerfully from inside the box.
However the away team's lead only lasted two minutes when City captain Jamie McKenzie's free-kick from the left was headed home by the former Northern Irish U-21 international Hugh 'Shuggie' Dickson from short range.