Referee Darren Drysdale put the kick-off back an hour to give groundstaff at the Pirelli Stadium the chance to clear surface water using a machine borrowed from Derbyshire County Cricket Club.
Remarkably, the Cod Army scored all the goals in a end-to-end contest as they maintained their 100 per cent start to 2014.
David Ball and Nathan Pond twice put the visitors ahead - only for Burton to be rescued by own goals from Mark Roberts and Alex Marrow. Late goals from Jon Parkin and substitute Junior Brown then sealed victory for Alexander's side.
A delighted Alexander said: "We shot ourselves in the foot a couple of times and Burton put us under pressure as you would expect of a team with good attacking qualities.
"But we scored four goals in the right net - and I think we deserve to be going home with the three points.
"We play Scunthorpe on Monday, so we knew we had two really tough games.
"But we had to focus solely on this one, which we have done, and I thought the determination and effort from the lads was unbelievable.
"That was a game for big hearts and we showed that's what we've got.
"We know we've got quality. We got the lead twice and threw away and we could have started to think negatively, but we didn't and everyone deserves a great big pat on the back."
Dejected Burton manager Gary Rowett said: "First and foremost, that was by far the best Fleetwood have played in the four games we've had with them this season.
"The first half was a little bit disappointing from our point of view and then we went on to concede goals at poor times.
"We got it back to one-all and I have to be honest and say I was very disappointed with the decision to allow the second goal to stand because I thought it was a clear push in the back of (Burton defender) Ian Sharps.
"That gave us a little bit of a mountain to climb, but we got back in it at two-all and then had one or two chances I felt we should have made a little bit more of.
"We had all the pressure at that time and they were looking to hit us on the counter, which they did for the goals.
"But credit to Fleetwood, they worked very, very hard to get that result."
- Sports & Recreation