Aiming to end a 40-year stranglehold of Scottish football by Celtic and Rangers, Hearts cruised to victory in manager Derek McInnes's return to Rugby Park.
McInnes left Kilmarnock to join the Edinburgh side at the end of last season and has made a stunning start, winning 22 points from a possible 24.
Centre-half Craig Halkett's third goal in three games put the Jambos on course for victory.
Claudio Braga struck twice in quick succession early in the second half to ensure Hearts will go into next weekend's meeting with Celtic top of the table.
"No-one is getting carried away," said McInnes. "We just want to take care of each and every game.
"It looked straightforward in the end, but until the third goal went in, it wasn't."
Celtic can reduce the gap at the top back to two points when they travel to Dundee on Sunday.
Rangers are now 13 points adrift of the leaders as the sacking of Russell Martin had little effect on the struggling Glasgow giants.
Shanghai Port coach Kevin Muscat is expected to be named as the new boss at Ibrox in the coming days but he will reportedly not take up the role until the end of the Chinese season next month.
Under the interim charge of former defender Steven Smith, Rangers got off to a strong start thanks to Norway international Thelo Aasgaard's stunning strike.
However, Rangers are yet to win at home in the league this season and were heading for another damaging defeat when goals from Kristijan Trapanovski and Craig Sibbald put the visitors on course for victory.
James Tavernier rescued a point on 87 minutes but did not save the home side from a chorus of boos at full-time after a sixth draw in their opening eight league games.
"I think to go from the level in the first half where you're thinking you should be two or three goals up to coming away at the end where you're probably lucky to get a point is quite frustrating," said Smith.
Aberdeen moved off the bottom of the table thanks to Marko Lazetic's 96th minute winner to beat St. Mirren 1-0.
Hibernian thrashed Livingston 4-0 and Falkirk were 2-1 winners at Motherwell.