It was the home side who started brighter and should have taken the lead in the third minute when Adam Nelson's deflected cross was brilliantly saved by John Dodds.
Elgin took the lead in the 21st minute when Alan Dempsie's free-kick was nodded down by Hugh Dickson and Chris Gardiner supplied a neat finish.
East Fife levelled straight away in the 24th minute when good work on the right by Elliott Smith produced a good cross for Craig Lumsden to finish from close range.
Elgin seemed to disappear after this, and East Fife took the lead in the 30th minute when Marco Pelosi's cross found Kevin Gordon who controlled and finished from close range.
Against the run of play Elgin equalised in the 44th minute when a great ball thorough from Adam Nelson found Mark Booth, who finished coolly into the bottom corner.
In the second-half East Fife re-took the lead after only one minute when Paul Hampshire's free-kick was spilled by Kieron Renton and Craig Smart was on hand to finish.
In the 52nd minute the game changed again when Stuart Cumming cut the ball back for Booth to equalise.
Elgin then introduced trialist Gary Tweedie and he didn't take long to make an impact. In the 66th minute Nelson and Stuart Cumming worked a short corner and Nelson's cross found Tweedie, who volleyed into the top corner.
Booth put the game out of reach and sealed his hat-trick in the 80th minute with a fine run and finish.