A brace from the in-demand Gary Hooper helped secure the points for Celtic.
The striker wanted by Norwich scored early from close in and sealed victory with a goal five minutes from time.
Georgios Samaras gave Celtic a two-goal lead in 12 minutes, but Hearts gave Celtic a scare when Jason Holt's deflected shot reduced the deficit.
Hooper's late contribution put the game beyond the visitors and substitute Lassad rounded off the scoring in style in injury time.
Celtic had looked in the mood from the off and delivered notice of their intentions within 90 seconds.
Adam Matthews took advantage of a kindly break of the ball inside the box to roll the ball to Hooper, who stretched to tap into Jamie MacDonald's empty net.
Celtic were exploiting a weakness down Hearts' left and that was the source of the home side's second, with only 12 minutes on the clock.
Kris Commons got away from Kevin McHattie, though the Celtic player was fortunate not to be penalised for pulling his opponent back.
The referee Iain Brines saw nothing wrong and Commons' shot from inside the box was parried by MacDonald, but only into the path of Samaras who simply had to roll the ball into the empty net.
Celtic were utterly dominant and only occasional carelessness gave Hearts the slightest glimmer of hope.
The home side should have had at least a third goal before half-time, with Commons scuffing a shot straight into the arms of MacDonald and then Joe Ledley having an effort blocked by Andy Webster, with the goalkeeper grounded.
Jamie Walker was introduced at half-time by John McGlynn in place of Callum Paterson and he instantly made an impression, forcing Lukasz Zaluska into action for the first time in the game, the Pole saving low to his right.
Hooper thought he had his 20th goal of the season when he converted Commons' cross from the left, but an offside flag curtailed his celebrations.
Celtic should have been celebrating a third goal just before the hour mark when Matthews picked out the unmarked Scott Brown eight yards from goal, but the captain's diving header was well off-target.
Moments later, MacDonald produced a superb save to keep out Ledley's powerful shot - the culmination of another excellent Celtic move.
Having failed to put the match beyond the visitors, Celtic found their lead halved on 69 minutes.
Holt picked up a long clearance from MacDonald and with the Celtic defenders trying to close him down, he poked the ball goalwards and courtesy of a wicked deflection, found the bottom right corner of the net.
Hearts searched for an equaliser in vain and Hooper did get his 20th goal of the campaign, firing low past the keeper after a powerful run by Brown down the right.
Lassad gave the scoreline a more impressive look in injury time when he found the net in stylish fashion from a tight angle, beating MacDonald with a beautifully controlled finish.
Hearts gave their all throughout, but were ultimately outclassed, though the addition of Danny Wilson already looks an astute one by John McGlynn.