A goal from striker Jack Hamilton, on loan from Livingston, on 56 minutes gave the Red Lichties all three points at Gayfield over their nearest challengers Killie.
Hamilton’s effort from just outside the penalty box lacked power, but it squirmed past Killie keeper Zach Hemming and into the net.
Arbroath ended the match with ten men after James Craigen was dismissed five minutes from full time, but Dick Campbell’s men held on for what could be a crucial three points in the title race.
"I thought we shaded it over the night,” said Campbell. “I’m very, very happy, and let’s see where that brings us.”
Arbroath next face Hamilton in the league on Wednesday before taking on Hibs at home in the last 16 of the Scottish Cup.