The striker grabbed the only goal of a poor game to give Dunfermline a precious three points at the foot of the table.
Dunfermline had a narrow escape after 15 minutes when Allan McGregor let a Richard Foster cross slip through his fingers but the home defence scrambled the ball clear before Darren Mackie could cash in.
Kyle Macaulay then beat the offside trap but failed to control Kevin McNaughton's through ball and McGregor managed to clear.
Aberdeen looked the more likely and Foster tugged a 25-yard shot wide with McGregor off his line.
Russell Anderson then came within inches of the opener when he met a Scott Severin cross at the back post, but his header slipped narrowly wide.
But Dunfermline came back and Anderson did well to block a netbound shot from Burchill after good work from Scott Muirhead.
From Muirhead's resultant corner, Noel Hunt had a free header but sent it over the top from 15 yards.
Dunfermline made the breakthrough after 48 minutes when a mishit shot from Hunt broke to Burchill and he scored from close-in.
Burchill hit the crossbar moments later with a header from only two yards and, in spite of late pressure from Aberdeen, Dunfermline held on.