The Tweedsiders looked to have it all to do in the second period, two goals down and reduced to 10 men, with Dean Boyne sent off midway through the first half, writes George Riley.
However, goals from Dean Clark and Steven Tait secured an unlikely draw.
Manager Scott Dowie commented after the game: “I asked the boys for a reaction at half-time and I’m glad to say the team responded well.
“It was an excellent effort by all the players, showing grit, determination and the willingness to work for one another.
“Hopefully, this will give us a bit of confidence to build upon.”
The Fifers opened the scoring with 10 minutes gone, Ewan Henderson finding his striking partner Adam Doig in space. The No9’s shot hit the inside of the post before nestling in the net behind Elliott Turnbull.
Kelso went down to 10 men just before the half-hour mark as Boyne was given his marching orders by Edinburgh referee Daniel Graves. Having already been booked the midfielder got involved in a fracas with Brendan Napier.
Burntisland increased their advantage six minutes from the break as Napier slipped past a couple of defenders before crossing to Shaun Keatings, who bundled the ball over the line.
United were awarded an indirect free kick in the 67th minute as Fife keeper Jordan Mushet got in a tangle from a pass back and handled the ball in the box. At the left side of the area, Liam O’Rourke laid the ball into the path of Dean Clark and the big defender’s shot thundered into the top corner of the net.
The home team equalised with two minutes of the match remaining. A free kick was awarded at the junction of halfway and touchline. Turnbull launched the ball to the back post, where Steven Tait met it in full flight, his header flashing past the despairing Mushet.