The home side were missing Ryan Donnelly, red carded against Dumbarton last week and ex-Diamond Ryan Wallace was missing for the visitors.
In what was a drab first half, both sides couldn’t capitalise on the few chances they created.
Willie McLaren saw his cross go wide, whilst Craig Johnstone had a shot blocked by Diamond’s skipper Paul Lovering.
Jamie Stevenson attempted a dipping shot but it didn’t dip low enough to give the home side an advantage.
They got their advantage five minutes into the second half when John Boyle played in Sean Lynch who squeezed through the defence to make it 1-0.
Scott Morton, who came in for Donnelly in the line-up, should have made it 2-0 with an almost identical move but his shot went wide.
East Fife’s makeshift forward line of Dalziel and McQuade had a few chances again but they weren’t getting anything past Grant Adam, the keeper staying in the side despite being stretchered off only a minute into his midweek appearance for Scotland U21s.
Two minutes from time Bain got the ball at the edge of the box and cut inside with his right foot to hit it in the bottom left corner past keeper Michael Brown.
Shortly after McLaren and White were given their marching orders for going nose to nose after a late challenge on the former.
The win keeps Airdrie in 4th spot, two goals ahead of Stenhousemuir going into next week’s crucial last fixture against champions Cowdenbeath.
Gordon Durie’s East Fife could also find themselves in the mix, but today’s defeat puts them three points and eight goals behind the Diamonds (and six goals behind the Warriors who play Forfar).