Midfielder Callum McGregor, who only started because Stuart Armstrong pulled up injured in the warm-up, opened the scoring with a well-taken goal on the half-hour mark.
Patrick Roberts scored in between a Scott Sinclair double - the second from the spot in the dying minutes - as Brendan Rodgers’ side extended their unbeaten domestic run since the start of the season to 27 games, one more than Jock Stein’s all-conquering side of 1966/67.
That the Hoops cruised to victory without recognised strikers Moussa Dembele and Leigh Griffiths, out with respective knee and calf injuries, and Armstrong, is testament to Celtic’s power in Scotland and the 17th consecutive league victory restored their 22-point lead at the top of the table over Old Firm rivals Rangers.
Rodgers initially made only one change to his side, Roberts replacing Dembele with winger Sinclair leading the line but Armstrong’s injury meant McGregor was brought in with left-back Emilio Izaguirre joining the substitutes.
Stoke City’s 21-year-old winger Moha El Ouriachi Choulay, signed on loan until the end of the season on Saturday, started on Hearts bench as did fellow new boy Dylan Nguene Bikey.
In the 16th minute of a low-key start to the game, Hearts defender John Souttar was robbed inside the box by James Forrest when he dallied in possession and was relieved to see the offside flag up when the loose ball fell to Sinclair 12 yards from goal.
Roberts was causing problems for the Edinburgh side down the right-hand side but it was Sinclair’s good work through the middle which led to the opener.
The former Manchester City player sent McGregor through on goal with a fine pass and he quickly knocked the ball past keeper Jack Hamilton and in off the post for his third goal of the season.
Occasional moments of slackness in the Celtic defence offered some hope for Hearts and seconds before the interval Jamie Walker headed an in-swinging Malaury Martin free-kick just over the bar from 12 yards.
Roberts switched to centre-forward for the start of the second-half in which the Tynecastle side found themselves under immediate pressure, full-back Liam Smith getting a saving tackle on Forrest as the winger set himself to pull the trigger 10 yards out.
As Celtic stepped up the pace further, Sinclair’s cross looked like it might have struck the arm of Souttar before going behind but referee Bobby Madden gave the corner.
Most of the heat had left the home side’s attacks but in the 69th minute Roberts fired wide from just outside the box, while moments later at the other end, Craig Gordon pulled off a fine save from Martin’s drive, following a Gorgie counter.
As play stretched, Sinclair should have made it 2-0 from left-back Kieran Tierney’s cross to the back post but failed to connect properly and missed the target.
However, after defender Aaron Hughes blocked another cross from Tierney to almost put the ball into his own net, the Hoops winger bundled it over the line and when Tierney again raced down the left, this time he picked out Roberts with a pass and he hammered the ball high into the net from 10 yards.
With minutes remaining Souttar was carried from the field on a stretcher after picking up an injury, leaving the visitors to finish the game with 10 men as they had used up their three substitutes.
However, there was time for Sinclair to slam in a penalty after Tynecastle defender Lennard Sowah fouled Hoops substitute Jack Aitchison, who had replaced Roberts, inside the box, completing a miserable day for Hearts and a record-breaking afternoon for Celtic.