Goodwillie was on target as United secured maximum points at Rugby Park
David Goodwillie was on target as Dundee United claimed three Scottish Premier League points with a hard-fought victory at Rugby Park.
The striker broke the deadlock after 15 minutes when his shot took a deflection before beating goalkeeper Cammy Bell.
Connor Sammon fired wide and Craig Bryson also came close to levelling.
Jon Daly doubled United's lead before Killie defender Frazer Wright was sent off for a second bookable offence and Sammon grabbed a late consolation.
United's victory was their third in a row in all competitions and keeps them fourth in the SPL, two points behind Motherwell, while Killie remain eighth.
Scott Severin tried to score against his former club with a firm header in the fifth minute but home keeper Bell held well.
Severin then made an important tackle at the other end to block David Silva's shot.
Prince Buaben's powerful free-kick drew a save and was gathered by Bell and United keeper Dusan Pernis also needed two attempts to claim Danny Invincibile's low drive.
The visitors moved into the lead on the quarter-hour mark when Paul Dixon's perseverance resulted in the ball running kindly for Goodwillie, whose shot looped over Bell via a defender.
Sammon almost levelled when his header from Silva's cross just cleared the crossbar.
The forward then dragged a shot wide after exchanging passes with Bryson.
After Alexei Eremenko blasted a volley off-target, Kilmarnock threatened again when Silva's long-range shot brought out the best in Pernis.
Killie appeals for a penalty were turned down after Eremenko went down in the box when challenged by David Robertson, who headed wide of the home goal just after the break.
Silva blazed high and wide of goal and Manual Pascali and Eremenko were also unsuccessful with attempts at the United goal before Bryson passed up a great chance to score from Jamie Hamill's accurate cross.
And this profligacy was punished when Daly latched on to Severin's knockdown and scrambled the ball over the line.
Wright was dismissed after picking up two bookings in the space of eight minutes, the second yellow card shown for dissent.
Sammon raised hopes of a comeback in injury time when he bundled the ball over the line after meeting Rui Miguel's cross but it was too little, too late for Kilmarnock.
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