Hoops midfielder Olivier Ntcham opened the scoring on the half-hour mark at Celtic Park.
Second-half goals from Christopher Jullien, Callum McGregor, substitute Ryan Christie and Jozo Simunovic completed the rout for Neil Lennon’s side.
Hearts substitute Marcel Langer was shown a straight red card by Willie Collum late on for a foul on Scott Brown.
The biggest cheer of the night came when news of Kilmarnock’s decisive late goal against second placed Rangers came through, with Steven Gerrard’s side now 10 points behind the champions, albeit with a game in hand.
“It might give them a bit of confidence but that’s about it,” Lennon said of the night’s significance in the title fight.
“We have a tough game on Sunday at Aberdeen. We are taking absolutely nothing for granted.
“The players know there is a long way to go and there will be twist and turns as we go along.
“We just need to concentrate on every individual game as it comes along. They were magnificent tonight. It was an emphatic victory.”
Ayrshire was famously the venue where the wheels came off for Rangers during last season’s title race and they were left with another dose of Rugby Park regret.
A ground where Rangers had won just once in their six previous league visits could yet prove to be the graveyard for this year’s aspirations as goals from Stephen O’Donnell and Eamonn Brophy saw them slip well adrift of Celtic.
The Ibrox side still have two Old Firm clashes to play but Celtic will believe they have one hand on yet another title.
Scott Arfield had fired Rangers ahead but Kilmarnock took advantage of the visitors’ nerves to claim a victory which keeps them just a point outside the top six.
“I thought we were in a better place than what we’ve shown over the last four to six weeks,” Gerrard said.
“I thought we had the mentality and the characters to sustain a push but on the evidence of the last four-five weeks I’m getting proven wrong.
“But having said that, it’s me as well because I’m responsible for that group of players.”
Asked where the defeat leaves Rangers in their quest for a first league title since 2011, Gerrard added: “Very, very tough. You’ve got to look at the form of other people that are relentless right now.
“There’s no denying they’re obviously in the driving seat.”
Livingston shrugged off their Scottish Cup exit at the hands of Championship opponents Inverness as they beat St Mirren 2-1.
Hibernian claimed consecutive victories for the first time since November as they swept aside Ross County 3-0 at Easter Road.
Substitute Chris Kane scored a stoppage-time winner as St Johnstone beat 10-man Motherwell 2-1.
