David Gold's ninth-minute effort was enough for the Red Lichties to extend their unbeaten run in the league to seven matches.
Ryan Dow and Graham Dorrans missed two early chances for Dunfermline before Arbroath took the lead at Gayfield. Jack Hamilton's low cross from the left was swept home by midfielder Gold for his second goal of the season.
The Pars, who are now bottom of the table, could have equalised just before the break but Steven Lawless hit a post when through on goal.
Lewis McCann also rattled the goal frame in added time for Dunfermline but the home side held on for a vital three points.
Fraser Murray and Blair Alston scored either side of the break as Kilmarnock kept the pressure on Arbroath with a 2-0 victory at home to Hamilton Accies.
The home side just edged first-half possession and enjoyed five shots on target to the visitors' none as Rory McKenzie came close with two efforts in the opening 15 minutes.
Stephen McGinn saw his header saved midway through the first period, while Murray just missed the target with a chance that sailed over the crossbar minutes later.
Kilmarnock's pressure paid off as Murray broke the deadlock on the stroke of half-time as he slotted the ball into the bottom corner from very close range thanks to Chris Burke's assist.
Former Hamilton midfielder Alston doubled the hosts' lead ten minutes after the break as he fired home Oli Shaw's cross to net against his old side and seal maximum points.
James Maxwell scored twice as Ayr United eased to a third successive away win with a 4-0 victory at Raith Rovers. A devastating first-half display saw the visitors lead 3-0 at the break.
They made a flying start as Tomi Adeloye rifled the ball into the roof of the net from Sam Ashford's low cross in the third minute.
Rangers loanee Maxwell doubled their lead as he finished off a swift counter-attack with a low drive and grabbed his second of the game after 38 minutes with a close-range finish from Mark McKenzie's pass.
Ross Matthews and Ethan Ross had early second-half chances for Raith as they looked to get back into the game. But Ayr added a fourth after 65 minutes when Ashford dinked the ball over goalkeeper Jamie MacDonald from Jordan Houston's ball forward.
Queen of the South improved their survival hopes by beating Morton 3-0 at Palmerston Park.
The hosts took the lead in the 19th minute through on-loan Motherwell full-back Max Johnston, whose powerful shot from just outside the box was too strong for goalkeeper Jack Hamilton to keep out.
The lead was doubled just past the half-hour mark when Josh Todd's ball sent Aidan Fitzpatrick racing clear and he calmly beat Hamilton. Ruari Paton made the points safe seven minutes into the second half from the penalty spot after Hamilton had brought down Ruben Soares Junior.