Both sides had chances before the Pars' Ryan Wallace drilled a low shot into the bottom corner with 15 minutes left.
The lead last just two minutes as Ross Davidson got the last touch on a free-kick into the area.
The home side dominated the closing stages but could could not deny Rovers, who remain in fifth place.
Rovers remain level with Airdrieonians, who drew at home with Forfar Athletic.
Scottish League One leaders Dunfermline Athletic were held at home by Albion Rovers but still moved 11 points clear at the top of the table.