Robbie Keane missed a host of chances to score his first goal in front of the Celtic support as the home side cruised the second half but there was no harm done.
Indeed, with Rangers drawing 1-1 at Motherwell, Celtic nudged closer to their Ibrox rivals and deservedly so after an indifferent first half.
Diomansy Kamara and Edson Braafheid were also making their first starts at Celtic Park. The stadium was slightly busier than usual - mostly due to the presence of Keane, who had got off the mark with a penalty in Sunday's Active Nation Scottish Cup fifth-round win at Dunfermline.
Hearts had beaten Celtic twice already this season although they were still looking for their first win under boss Jim Jefferies, back at Tynecastle for the second time.
The 'Keane effect' failed to lift the home side in the early stages as the Edinburgh men were allowed to settle in to the game.
In the eighth minute the Irishman had the first chance of the game when he beat the offside trap to race onto a long Josh Thompson pass but he blasted his angled volley in to the side-netting from 10 yards.
The Gorgie men fed off the tension which was slowly taking a grip of the Hoops players as Celtic struggled to get into their stride.
Keane was caught offside a couple of times by the visiting defence, who had clearly tightened up following their early escape.
In the 26th minute, though, Kello was the Hearts hero when he made a double save, first from Scott Brown when the Celtic captain tried to chip him from eight yards out and then from Fortune, who blasted the rebound off the stopper for a corner.
Moments later, Kello made yet another good save when he blocked Keane's effort after the Irishman was sent clean through on goal by Aiden McGeady.
Celtic then had a narrow escape when Hearts debutant Ryan Stevenson's mis-hit shot from 30 yards was re-directed towards the Hoops' goal by the unmarked Paul Mulrooney, the ball flashing just wide of the target.
McGeady picked up a booking from referee Brian Winter, apparently for dissent, after the half-time whistle sounded which summed up Celtic's frustration.
The home side came out for the second half buoyed by the news that Rangers were losing at Motherwell and were boosted further when they soon found themselves two goals up within the space of a minute.
Four minutes after the restart Kamara swung a corner over from the right and from 10 yards out Loovens had two attempts to get his shot in, the second one whistling in to the net.
A minute later, with the Jambos still in disarray, McGeady sent Fortune clean through down the right channel and he drove into the box before slipping the ball past Kello.
McGeady should have made it 3-0 when he was put in by Keane but the midfielder fired wide from just inside the box.
As Hearts all but crumbled, Keane missed another chance, again from a tight angle.
In the 62nd minute new signing Thomas Rogne replaced Loovens to make his Celtic debut.
It looked like it was going to be one of those nights for Keane as he missed another two opportunities to get his first goal in front of the Parkhead crowd.
McGeady tried time and again to set up his Republic of Ireland captain but it simply would not fall right for the on-loan Tottenham man.
With seven minutes remaining he blasted over the bar from 10 yards when it looked he would at last get his goal but the points were secure and progress had been made.