The early chances fell to Eyemouth, who were searching for their second league win of the campaign.
With a good flowing passage of play the ball fell at the feet of Alan Jess, but his shot went past the left hand post.
Jess also had a second opportunity, but on this occasion missed to the right.
In the 42nd minute the deadlock was broken when a floated free kick from the right hand side to the back post was headed into the back of the net to give the home side the lead.
Then, on the stroke of half time, Burntisland doubled their advantage with a second.
A through ball was played behind the Eyemouth defence and a moment of madness from the Fishermen’s keeper, Mutch, who rushed out of his box to intercept, resulted in the Shipyard centre forward getting there first and he calmly slotted the ball home into an empty net.
In the second half the game opened up and Eyemouth tried everything to get back in the game but they couldn’t put the ball in the back of the net, which has been a problem for most of the season so far, which meant the home side were able to hold out for the victory.