Gary Naysmith hailed the second-half performance from his side as amongst the best since he arrived at the club.
Naysmith’s men recovered from a Steven Logan first-half strike against Annan to take all three points thanks to second 45 goals from Nathan Austin and Derek Riordan.
It was a crucial win for East Fife and now takes them to just one point behind their fourth place visitors in the final play-off spot.
Naysmith said: “We weren’t at our fluent best in the first half but I thought we were the better team.
“At half time we told them that not much had gone wrong.
“From the first minute of the second half we were relentless and camped in their half.
“That’s as good a 45 minutes I’ve seen at East Fife since I’ve been here as a player or as a manager.
“The lads were different class and there’s a big belief that when we go a goal behind we still aren’t going to lose.”
East Fife dominated the early game and were presented a great chance within the opening 10 minutes when the ball broke kindly to Ross Brown inside the Annan box.
But the midfielder got underneath his effort and scooped the ball high over the bar.
Austin was the next to go close for the home side when he headed an Alan Cook free-kick over the bar.
But it was Annan who broke the deadlock and did so in stunning style.
Peter Weatherston teed up Logan on the edge of the East Fife box and the midfielder lashed home an unstoppable effort past Allan Fleming.
East Fife dusted themselves down at the break and remained in pursuit of their first goal of the game.
Liam Smith and Cook went close for Naysmith’s men – but they were eventually to be rewarded for their persistence.
Sub Allan Walker played a crafty cross field ball straight into the path of Austin who composed himself before slamming past Jordan Hart.
A familiar trait of the Fifers in the past few weeks has been how strong they finish games and this was evident again at the weekend.
Sub Derek Riordan showed glimpses of the class which won him top class moves earlier in his career when he came on and it was the trialist who wrapped up the win when he flicked his effort past Hart in the closing minutes.