After Hearts dropped points earlier in the day, goals from Johnny Kenny, Kieran Tierney, Daizen Maeda and Arne Engels, with an added-time penalty, condemned Kilmarnock to a fifth consecutive defeat as they dropped to 10th.
Hearts drew 1-1 at home against Dundee United, their second draw in three matches.
Alexandros Kyziridis' shot rebounded off a post and deflected into the net off United goalkeeper Yevhen Kucherenko, only for Luca Stephenson to equalise just before half-time.
New Rangers manager Danny Rohl enjoyed a third successive league win, 3-0 over Dundee, to move 12 points behind Hearts with a match in hand and five behind arch Glasgow rivals Celtic, who've also played 11 league games.
Nico Raskin headed home a ninth-minute corner, and Mikey Moore doubled the lead with his first goal since joining on loan from Tottenham Hotspur before Djeidi Gassama curled home the third in the 90th minute.
Motherwell made it three unbeaten in the league with a 1-1 draw at Aberdeen, Elijah Just cancelling out Jesper Karlsson's opener for the Dons.