Ange Postecoglou has taken another major step with Celtic towards a successful Scottish title defence on a day when Ryan Strain scored for St Mirren in a Premiership battle of the Socceroos.

Portuguese star Jota proved Celtic's trump card at Parkhead, scoring on the stroke of halftime to end Kilmarnock's dogged resistance before the champions went on to win 2-0 on Saturday, a victory that thrusts them 12 points clear at the top.

For 44 minutes, Killie kept the leaders at bay but Jota netted from close range in the final minute of the half, before Kyogo Furuhashi bagged his sixth goal in as many games shortly after the interval, although his finish did take a big deflection off Killie defender Ash Taylor.

Postecoglou's men could have scored more but did enough to heap more pressure on Rangers ahead of their rivals' trip to Dundee United on Sunday.

And they laid down a marker before playing Kilmarnock again next weekend in the League Cup semi-final at Hampden Park.

"We're comfortable where we are, but we know there are still 17 games to go," said Postecoglou.

"We want to finish the season stronger than we started. We have a cup semi-final to look forward to now. It's unusual to be playing the same team two weeks in a row but it will be a different set of circumstances and a different challenge. It will be a special day."

While midfielder Aaron Mooy was influential for Celtic, four of his Socceroos' teammates were at the heart of a 1-1 draw between St Mirren and Hearts.

The contest brought together St Mirren's Keanu Baccus and Ryan Strain face to face with the Hearts pair of Cammy Devlin and Kye Rowles, with the Edinburgh side's third Socceroo Nathaniel Atkinson on the bench.

There was an early Australian flavour to the game when St Mirren earned a fourth minute free-kick after Devlin had tripped Baccus and Strain stepped up to strike home the 20-metre opener with a bit of help from a deflection off Toby Sibbick.

Hearts nearly equalised 10 minutes before halftime but Rowles couldn't quite get enough on his close-range header from Robert Snodgrass's free-kick.

But four minutes after the break, Snodgrass's inswinging left-footed cross from the right eluded everyone and nestled in the corner of the net - his first goal for the club - as Hearts maintained their third place in the league, 14 points behind Rangers.