After David Goodwillie put United ahead on 15 minutes, Kilmarnock dominated the first half and again after the break before United doubled their lead on 69 minutes through Jon Daly.
Kilmarnock ended the game with 10 men after two late bookings for Frazer Wright, before Conor Sammon's injury-time goal for the hosts.
Garry Kenneth had recovered from a head knock to take his place alongside Darren Dods at the back for the visitors - but Craig Conway, whose medial ligament damage flared up in training, missed out.
Killie demoted on-loan Chelsea defender Ben Gordon to the bench to allow veteran Garry Hay a return at left-back.
The last time these clubs met at this ground in January the match finished 4-4 - so this Clydesdale Bank Premier League contest had much to live up to.
Scott Severin, on loan at Kilmarnock from Watford last season, was the first to threaten for the visitors with a firm header well held by Cameron Bell.
David Silva nutmegged Kenneth, sporting a head bandage, but his driven shot in the fifth minute was blocked by a diving tackle from Severin.
Kilmarnock goalkeeper Bell needed two attempts to catch a powerful Prince Buaben free-kick, as did his United counterpart when dealing with Danny Invincibile's low drive.
United were ahead in the 15th minute when battling play from Paul Dixon saw the ball run kindly for Goodwillie and his deflected shot looped over the grounded Bell and in.
Killie came close to levelling when Silva made room on the left and, from his cross, Sammon sent a flicked header over the crossbar.
Sammon was looking Kilmarnock's main threat and after exchanging passes with Craig Bryson he sent a shot narrowly wide with goalkeeper Dusan Pernis beaten.
Kenneth did well to get in the way of a fierce effort from Silva, but might have been punished when he seemed to impede Sammon's attempt to retrieve the loose ball before Pernis.
Alexei Eremenko was frustrated when Invincibile failed to control his crossfield pass, but did not fare much better himself with an attempted volley from distance which flew well off target.
Silva connected much better with a long-range shot on 40 minutes, Pernis this time forced into an acrobatic one-handed stop to preserve United's advantage.
Kilmarnock had a penalty appeal rejected when David Robertson felled Eremenko inside the area, but any contact was minimal and it looked the correct decision to give nothing.
United made a change at the break with Dods, injured by a first-half challenge by Sammon, making way for Scott Robertson.
On 48 minutes, United should have doubled their lead, Goodwillie's low cross from the right seeing David Robertson send a diving header wide from close range.
Back came Kilmarnock, but again their finishing was wasteful as Sammon played in Silva for a shooting chance, but the winger blazed high and wide.
Manuel Pascali had a shot deflected wide by Kenneth, while an angled Eremenko drive drifted beyond the far post as a goal remained elusive for the home side.
Jamie Hamill's good work on the right and resulting cross deserved better than Bryson's poorly struck shot wide with the goal inviting.
The United punishment for misses like these came in the 69th minute when - after Severin's headed knockdown - Daly controlled and scrambled the ball over the line.
Kilmarnock's fate was sealed when Wright collected a second yellow card and an ordering-off in the 82nd minute for dissent, although Conor Sammon did get the home side on the scoresheet in the third minute of injury-time when he bundled in a Rui Miguel cross which was headed back in by Silva.