Nathan Austin headed home a cross from Joe Cardle in the eighth minute, which proved enough for all three points.
Stirling moved up into second place as they thumped bottom club Cowdenbeath 4-0 at Forthbank Stadium.
Jack Leitch put Albion in front after just six minutes, slotting in from close range after his initial header hit the bar, and Dylan Mackin doubled the lead before half-time.
Substitutes Dale Carrick and Sean Heaver added two more in the closing seven minutes as Stirling went above Annan, who slumped to a 3-1 home defeat against Edinburgh City and finished with 10 men.
Ouzy See set the visitors on their way after 10 minutes, with James Hilton adding another ahead of the break.
John Robertson added a third following a free-kick in the 68th minute.
Matty Douglas was dismissed for a second bookable offence with 15 minutes to go, before Annan substitute Robert McCartney hit a late consolation.
Forfar got back to winning ways as they beat Albion 3-1.
Stefan McCluskey gave the Loons an early lead, before two goals in the space of four second-half minutes just after the hour from Scott Shepherd and Matthew Aitken put them in control.
Albion pulled a goal back with eight minutes left through a trialist, who had come off the bench.
Stenhousemuir slumped to a third defeat in four league games as they were beaten 2-1 at home by Elgin City.
The visitors took the lead after only four minutes when defender Darryl McHardy headed in from a corner.
Nicky Jamieson nodded in an equaliser with 20 minutes left, but Russell Dingwall wrapped up the points for Elgin late on.