Killie arrived at Celtic Park with only two points gained on the road this season but gave the home side very little encouragement in the opening 44 minutes.
However, Jota netted from close range in the final minute of the half and Kyogo Furuhashi bagged his sixth goal in as many games shortly after the interval.
The champions threatened to score several more as they put further pressure on Rangers ahead of their nearest challengers' trip to face Dundee United on Sunday.
There was a pre-match tribute on the big screens to Frank McGarvey following his death on New Year's Day and the former Celtic striker shared a minute's silence with Pele and Pope Benedict XVI.
Celtic manager Ange Postecoglou brought in Alexandro Bernabei for the injured Greg Taylor, while Aaron Mooy and Jota were also recalled.
Postecoglou claimed on Friday there was "zero chance" major penalty decisions against his team would even themselves out over the course of the season and Killie had an appeal inside 30 seconds when debutant striker Kyle Vassell went down under the attention of Carl Starfelt. Nick Walsh played on after a VAR check.
Killie lined up with five at the back and defended from the front to deny the Celtic midfield time on the ball.
The tactic worked for the vast majority of the first half. Celtic took 20 minutes to force a corner and another five before getting their first effort at goal, when Jota's deflected effort was easily held by Sam Walker.
The visitors also had some moments going forward. Chris Stokes' cross hit the top of the crossbar and Ash Taylor headed on to the roof of the net.
Celtic had a goal disallowed in the 41st minute when Jota was called offside from Mooy's lofted pass after the Portuguese winger's low cross was turned home by Furuhashi.
But the decision looked straightforward and the away side looked like deservedly going in level at half-time until Bernabei's pass sent Daizen Maeda in behind Lewis Mayo. The Japan international cut the ball back and Jota knocked it home from close range after Furuhashi had slid in front of Walker.
Walker blocked Jota's shot with his foot after the break but he was beaten in the 51st minute following a counter-attack.
Reo Hatate overlapped Mooy and received a pass before sending in a low cross which was diverted towards goal by Furuhashi. The shot appeared to take a deflection before finding its way into the back of the net.
That was effectively game over and the rest of the contest saw Killie trying to keep the score down amid near-constant Celtic pressure.
They managed to do so despite a series of close shaves. Maeda could not make the most of several chances, Walker made a good stop from Hatate's 22-yard drive and substitute Liel Abada flashed an effort wide from similar distance.
The chances kept coming for the substitutes. Giorgos Giakoumakis saw a powerful header brilliantly saved and then hit the bar from long range, James Forrest hit Walker and then the post from two glorious quickfire opportunities and the goalkeeper pushed Matt O'Riley's close-range effort onto the post.
Callum McGregor and Forrest missed further good opportunities to capitalise on Celtic's second-half dominance before David Turnbull came close from l25 yards.