Annan opened the scoring after 66 minutes from the penalty spot. John MacBeth was tripped in the box by Nick Gray and Lewis Sloan stepped up to drive home the opener.
Having earned the penalty, MacBeth capped a productive day when he added Annan
's second goal in the 73rd minute with a fine finish after a flowing move.
To make things worse for the visitors, Chris Hegarty was sent off in the closing stages for a second bookable offence.
Queen's Park 1 Stranraer 2Substitute Martin Jack scored in the last minute for Stranraer to earn a 2-1 win over Queen's Park. Barry Douglas had put the hosts ahead in the 34th minute with a crisp volley.
The game took a controversial twist in the 50th minute when the Spiders' Ritchie Sinclair was sent off for hauling down Stuart McColm in the box. Danny Mitchell missed the resulting spot kick but Michael Moore soon levelled for Stranraer with a powerful header.
The match seemed destined for a draw before Jack headed Stranraer's dramatic late winner.
Elgin City 0 Albion Rovers 2First-half goals from David MacFarlane and Mark Canning helped Albion Rovers to a 2-0 win at Elgin. The visitors now hold a two-point lead at the top of the table.
Forfar Athletic 0 Livingston 1Troubled Livingston earned a hard-fought 1-0 win at Forfar thanks to an early goal from former Aberdeen striker Robbie Winters.
East Stirlingshire 1 Berwick Rangers 0East Stirling leapfrogged opponents Berwick Rangers into second spot after a nervy 1-0 win at Ochilview.
Livewire striker Andy Rodgers grabbed the winning goal just seconds into after the interval.