Hamilton fought back after losing an early goal and their goalkeeper through injury, to stage a second-half rally that earned them a share of the points.
East Fife took the lead after four minutes when Steve Ferguson blasted in from the edge of the six yards box a Damiano Agostini corner headed down by Steve Kerrigan.
Goalkeeper Ian Macfarlane was injured in blocking an effort from Ferguson six minutes later and limped off as teenager Stewart Thomson took over in goal.
And the young keeper went on to break the hearts of the East Fife strikers with a superb display on his debut.
Three times Thomson denied Ferguson and did well to save from Gallagher, Kerrigan and Brian McCloy.
Hamilton brought on Alex Eadie for young Michael Moore at half time and dominated the second half without cashing in on their advantage.
The vital goal came on 65 minutes when Eadie headed in a cross from Stuart Callaghan.
Ray McKinnon, booked for a first-half foul, was shown the red card for a second foul seven minutes from time.