Arbroath boss Allan Moore was disappointed that a late lapse took the gloss off what was shaping up to be one of the Lichties’ best performances of the season.
The League Two leaders played some outstanding football for 80 minutes as they pulled Annan apart and were well worth their 3-0 lead at that stage.
But the loss of two goals in the closing stages caused some worry in the home ranks.
Moore said: “We were 3-0 ahead then they got the two goals back and anything could have happened. It took the shine off what was a right good performance.
“I was ready to praise the boys for getting to 3-0, but then they switched off. Sometimes that can happen.”
The Lichties took the lead in 15 minutes when Bobby Linn cut in from the right and fired a dangerous low cross into the box which was deflected into the net by Annan’s Steven Black.
Moore’s side should have gone further ahead five minutes later, but Simon Murray guided his effort wide after being put through by Dylan Carreiro.
Annan’s best chances during the first half fell to Peter Weatherson, but he twice fired high over the top from good positions.
Jack Smith extended Arbroath’s lead in the 57th minute when he latched on to a loose ball and calmly slotted home below Alex Mitchell.
Carreiro showed great skill when adding a third shortly afterwards.
The Canadian under-21 international gathered the ball wide of the left and jinked his way past a clutch of defenders before executing a powerful and accurate finish.
It should have been game over but Annan refused to give up and, 10 minutes from the end, the visitors were given hope when Ryan McStay’s free kick from the edge of the penalty box went in.
The substitute Scott Davidson curled the ball into the top right-hand corner of Marc McCallum’s goal to further heighten the anxiety around Gayfield, but the Lichties were able to see out the final few minutes without any further trauma.