New Dundee United boss Craig Levein watched his charges claim their second consecutive SPL victory.
Dundee Utd's Noel Hunt scored the only goal of the game
In a dull first half Craig Conway's cross after good work from Mark Kerr just cleared the far post as the home side looked to open the scoring.
Noel Hunt got the breakthrough after 70 minutes when he drilled home Collin Samuel's cross from 18 yards.
Killie rarely threatened and Frazer Wright came closest when his header was blocked by Derek Stillie.
Utd were looking to continue their SPL revival with three points after coming from behind to beat Rangers the previous week.
The home side only sparked into life after the introduction of Collin Samuel, whose run set up Hunt's deserved winner with 19 minutes left.
Levein - in the dug-out after serving a touchline ban during his debut win
over Rangers last week - brought back Hunt from suspension and Stuart Duff, with
Greg Cameron and Samuel dropping to the bench.
Killie were missing Allan Johnston, with Rhian Dodds stepping in.
Nish turned and struck from 25 yards as Killie tried to hit back after Utd's opener but the ball
curled away from goal.
Gordon Greer headed just over his own bar after Robson's corner and the Killie defender soon had a half chance at the other end but his shot bounced harmlessly wide.
Robson cut in from the right but could not finish the game off as his
left-footed strike curled away from the far post.
Kilmarnock failed to penetrate the home defence as Craig Levein's men held on for victory.
Dundee Utd: Stillie, Mair, Kenneth, McCracken, Kalvenes, Kerr, Conway (Samuel 54), Duff, Robson, Hunt (Goodwillie 79), Robertson. Subs Not Used: McLean, Archibald, Cameron, Burnett, Smith.
Booked: Mair, Hunt.
Goals: Hunt 71.
Kilmarnock: Smith, Grant Murray, Greer, Frazer Wright, Hay, Invincibile (Stephen Murray 76), Fowler, Dodds (Ford 70), Leven (Di Giacomo 73), Nish, Naismith. Subs Not Used: Combe, Lilley, O'Leary, Adams.
Booked: Grant Murray.
Ref: W Collum.