Tam McManus's first goal for Dunfermline was enough to secure a victory that takes the Pars to within a point of second-bottom St Mirren.
United's Barry Robson sent a free-kick just wide, while Christian Kalvenes was denied by a Dorus De Vries save.
McManus had himself squandered a couple of chances before volleying home a Greg Shields cross after 34 minutes.
The Pars' Stephen Glass and United's John Daly went close after the break, but one goal decided the game.
McManus and Glass had returned to the Dunfermline starting line-up after being cup-tied for the Scottish Cup semi-final against Hibernian.
But strikers Jim Hamilton and Stevie Crawford, plus midfielder Stephen Simmons, were missing.
Morgaro Gomis returned to the Dundee United midfield in place of the suspended Mark Kerr.
However, it was Dunfermline who created the first threat after just 45 seconds, when goalkeeper Derek Stillie turned away a toe-poke by McManus, although the striker was ruled offside in any case.
McManus should have done better than head straight at Stillie after Jim O'Brien had beaten Kalvenes before sending in a dangerous cross.
Shields was next to find the head of McManus, but the former Dundee and Falkirk man's effort flashed wide.
The Pars missed a great chance to take the lead when Glass and McManus combined to set up Jim McIntyre just eight yards out.
But the former United man screwed his shot wastefully wide.
Levein's men offered their first real threat on goal in the 30th minute, when the cultured Robson curled a free-kick just inches wide of De Vries' right-hand post.
That gave the visitors a boost in confidence and Daly and Kalvenes exchanged passes in the Dunfermline box before the left-back was denied by a smothering save from De Vries.
The home side broke to the other end and immediately took the lead.
Shields charged down the right and crossed for McManus to volley home with great aplomb in the 34th minute.
United responded in spirited fashion but failed to especially trouble De Vries as Kenny's side held on for a slim advantage at the break.
Glass missed a glorious chance to extend Dunfermline's lead after the break when he blasted wide after a fine run had taken him past goalkeeper Stillie following a McManus through ball.
The Pars almost paid for that soon after, but Daly headed over from close range after De Vries failed to cut out a cross to the back post.
Dunfermline: De Vries, Shields, Wilson, Bamba, Glass, O'Brien (Daquin 90), Mason, McCunnie, Muirhead, McManus (Hammill 70), McIntyre (Burchill 85).
Subs Not Used: McKenzie, Ross, Young, Thomson.
Goal: McManus 34.
Dundee Utd: Stillie, Kalvenes, McCracken, Wilkie, Gomis (Easton 63), Cameron, Daly, Dillon, Robson, Samuel (Robertson 78), Hunt (Goodwillie 63).
Subs Not Used: McLean, Mair, Duff, McCord.
Booked: Gomis, Wilkie.
Att: 5,131
Ref: A Freeland