Aberdeen have missed the chance to go top of the Scottish Premiership after a 1-1 draw against Motherwell.
Adam Rooney headed in on the verge of half time but Scott McDonald equalised with 17 minutes to spare.
Hearts continued their assault on the top two after goals from Callum Paterson and Osman Sow led them to a win over fourth-placed Ross County.
Kilmarnock, who were adrift at the bottom of the table at the start of the season, have now won four of their last six matches. Josh Magennis scored early on before Steven Smith doubled Killie's lead shortly after the restart as they despatched Dundee. Rhys Healey pulled a goal back for the Dee late on.
Elsewhere, St Johnstone's Liam Craig scored a stoppage-time winner to defeat Inverness Caledonian Thistle 1-0 and Partick Thistle drew 1-1 against Hamilton Academical.
Celtic welcome Dundee United to Glasgow tomorrow.
Results in full: Aberdeen 1-1 Motherwell (1-0), Dundee 1-2 Kilmarnock (0-2), Hearts 2-0 Ross County (1-0), Inverness Caledonian Thistle 0-1 St Johnstone (0-0), Partick Thistle 1-1 Hamilton Academical (0-0)
