Jon Daly took his tally to 20 for the season with a double as the Tannadice side moved level on points with fourth-placed St Johnstone, who play Celtic on Sunday.
Scott Robertson was also on target against the Pars, who remain rooted to the foot of the table three points behind Hibernian.
United manager Peter Houston was without the injured Keith Watson and he was replaced by Robbie Neilson.
Czech striker Milos Lacny was also missing after suffering a cruciate knee injury in training, but captain Daly recovered from a head knock to play.
Dunfermline boss Jim Jefferies made two changes to the side that drew with St Mirren last weekend.
Kevin Rutkiewicz and Andy Kirk came in at the expense of David Graham and Liam Buchanan. New Spanish goalkeeper Bernardo Dominguez was missing from the squad.
The form of these two sides could not have been more different going into this vital clash.
United were looking to stretch their unbeaten run to nine SPL games, having recently racked up five successive wins, while Dunfermline - with just four wins all season - last celebrated a three-point haul back in January.
Jon Daly diverted Paul Dixon's cross wide inside 90 seconds as United started on top.
Home defender Gavin Gunning then stepped out of defence and sent a long-range drive fizzing past the post.
United kept pressing and Pars goalkeeper Chris Smith survived a scare in the 14th minute when his weak punch landed at Dixon.
The full-back's first-time shot came through a sea of bodies and landed on the wrong side of the post.
Less than a minute later, Neilson should have fired United ahead but he blazed over from six yards after being picked out by Gary Mackay-Steven.
Rutkiewicz earned the first booking in the 24th minute for a handball just outside the box but United made nothing of the free-kick.
The Pars weathered the United storm and finally managed to string some passes together.
They could even have taken the lead on 32 minutes but Alex Keddie's header from Joe Cardle's free-kick soared over.
That seemed to rouse United and Dunfermline goalkeeper Smith saved Mackay-Steven's 20-yard drive.
United began the second half with renewed enthusiasm and took the lead on 49 minutes.
Dunfermline failed to deal with Neilson's long throw-in and Daly's superb volley flew past Smith.
The Pars brought on Graham for Jordan McMillan in 64 minutes as they chased an equaliser.
But United almost grabbed a second when Johnny Russell headed Dixon's cross over.
Joe Cardle then threatened with a curling shot but Pernis had it well covered.
Robertson secured the points for Dundee United 10 minutes from time when he converted Mackay-Steven's cross after some great wing play.
And Daly rounded off the scoring in the closing stages when he pounced on Russell's pass to easily convert from close range.