Rory McAllister's free-kick fired the league leaders ahead after 16 minutes, before Annan's Ally Love missed a penalty. Two minutes after half-time, Andy Mitchell levelled for Annan before Kenny MacKay set up Love for a 55th-minute winner to move Annan within eight points of Peterhead.
That gap will be cut to five should Annan win their game in hand at Albion Rovers on Tuesday night. However, the Coatbridge club will be a considerable obstacle having thrashed struggling Elgin City 5-2 at Cliftonhill.
A Ciaran Donnelly volley and strikes from Liam Cusack and Gary Phillips gave Rovers an unassailable half-time advantage. Dennis Wyness reduced the arrears before Scott Chaplain's penalty restored Rovers' three-goal cushion. Shane Sutherland netted another consolation but Chaplain added his second and the hosts' fifth.
Third-placed Clyde are still on course for the play-offs despite a 3-0 defeat at Berwick Rangers. Lee Currie scored a double, having set up the opening goal for Darren Lavery, to fire Colin Cameron's side to within two points of fourth place.
Currently in that position are Stirling Albion who were held to a 2-2 draw by Montrose. Craig Comrie opened the scoring for Stirling in the 51st minute before Paul Watson equalised with a free-kick. David McClune's 83rd-minute strike appeared to have won it for Stirling but Garry Wood's last-gasp penalty salvaged a point for Montrose.
Bottom club Queen's Park won 4-1 at East Stirlingshire. Paul Quinn's opener for Shire was soon forgotten as Eamonn Brophy's double, Anthony Quinn's penalty and a Sean Burns goal clinched a superb Queen's Park victory.