United earned a point after a battling display in Fife with striker Jordan Hopkinson scoring the equaliser from a free kick five minutes from time.
The Tweedsiders were under the cosh for the first five minutes as the home side’s Dale Robertson headed wide, then keeper Elliott Turnbull had to dive full length to divert a goal-bound shot from John Paul McPhail.
Shipyard continued to press and Turnbull stopped a Robertson shot following good work by the home midfielders.
United’s best chance of the first half came two minutes before the interval as Jordan Hopkinson swung in a cross from the right and Andrew Oldham’s header was cleared off the line by Shaun Keatings.
The hosts started the second half on the front foot and Ewan Henderson went close with a shot that shaved the upright.
United began to get more into the game with an hour gone and Oldham went close again, firing a shot wide from a header by Ewan Hutchison. This was quickly followed by a Hopkinson shot from the left side of the box.
Midway through the second period Burntisland went down to 10 men as Brenan Napier received his second yellow card on the day for a foul on defender Darren Bowie.
The home side went ahead in the 74th minute as substitute Andrew McDonald picked up the ball in his own half and drove forward, and as the Kelso players stood back the defender unleashed a shot from 35 yards which hit the top corner of the net.
United eventually got the equaliser in the 85th minute when Hopkinson was upended at the edge of the box by Peter Bell.
Hopkinson got up dusted himself down and fired the free kick into the bottom corner with home keeper Barry Thomson well beaten.