Gary Naysmith feared his side were in a race against time to keep hold of the three points they earned at Galabank.
Annan offered little resistance to the flying Fifers, but with the snow falling heavily and settling on the artificial surface, Naysmith was glad to see out the 90 minutes as conditions worsened.
It would have been incredibly tough on Naysmith’s men, who simply destroyed their hosts to go in at the break four goals up, if the game had been abandoned late on.
Naysmith said: “I spoke to the ref at half-time and said that if the lines were cleared the pitch wasn’t any worse than when he started the game.
“If the ref thought it was dangerous he would have called it off.
“Until it got to about 75-80 minutes the pitch was playable but then a lot of snow started lying. But you certainly would have seen a protest from us if the game was called off with 10 minutes to go and we were 4-1 up.
“The ref showed a lot of common sense.
“We were happy for the game to go ahead, the only thing our lads were noticing was that they were having difficulty stopping.
“I said that to the referee and he said that wasn’t enough for him not to start the game.
“In general, although there was more snow on the pitch, it never got any slippier.”
The Methil men should have taken the lead with only five minutes on the clock.
With Falkirk gaffer Peter Houston watching from the stands, Nathan Austin’s run to the line would have impressed his new boss, who has loaned the striker back to East Fife.
Austin cut back for Jamie Insall who sidefooted wide from six yards.
Insall made up for his miss a few minutes later when he put the Fifers ahead.
Austin met a Gary Naysmith corner but his shot came back off the post and Insall was on hand to prod the ball home.
The snow then got heavier with the visiting support fearing ref John McKendrick may have a call to make.
East Fife made the ref’s life that little bit harder when they doubled their advantage.
Austin raced through the heart of the Annan defence and fired a shot low into Jordan Hart’s bottom corner.
The third goal game before the break to put East Fife on easy street, Jason Kerr heading past Hart and the points were in the bag before the interval when Kyle Wilkie finished off an Insall cross.
Austin had the chance to add the fifth early in the second half when he shrugged off the attentions of his marker but fired past the post.
In the final minutes Annan pulled a goal back when former Fife captain Greig McDonald fired home from outside the area. And they made the scoreline a lot more respectable when Peter Weatherston slammed home a second in injury time.