Celtic's lead at the top of the Scottish Premiership remains eight points heading into the winter break after scoring twice inside six minutes to beat 10-man St. Mirren 3-0 on Tuesday.

Rangers had earlier briefly cut the gap to five points with a 3-1 victory over Kilmarnock at Ibrox.

Philippe Clement's side have two games in hand to try and chip into Celtic's lead after a three-week shutdown.

However, the defending champions have hit their stride again in recent weeks after back-to-back defeats to Kilmarnock and Hearts last month threw the title race wide open.

Celtic were buoyed by their Old Firm victory on Saturday that inflicted Clement's first defeat since taking charge of Rangers in October.

Brendan Rodgers' men flew out the traps in Paisley as Daizen Maeda and Matt O'Riley slotted home from close range in an explosive start.

Any faint hope of a Buddies fightback was extinguished before half-time when Toyosi Olusanya was shown a straight red card for a studs up challenge on Celtic goalkeeper Joe Hart.

Greg Taylor added a third goal from Paulo Bernardo's pass on the hour mark and only wasteful finishing and the woodwork prevented Celtic from racking up a much more convincing margin of victory.

Rangers bounced back against in-form Kilmarnock as Abdallah Sima showed why he will be missed as he departs to represent Senegal at the Africa Cup of Nations.

Two goals in the five minutes before half-time swung the game in Rangers favour as Ross McCausland opened the scoring before Sima's finely struck volley registered his 15th goal of the season.

Danny Armstrong converted the first penalty Rangers have conceded in 75 league games to briefly bring Kilmarnock back into the match.

But Todd Cantwell quickly restored the home side's two-goal cushion.

Rangers could then afford to give loan signing Fabio Silva his debut.

And Clement promised there would be more new arrivals this month.

"We're going to do some more business," said the Belgian.

"Everybody in the club is aligned around that and we have now one month to do the good business."

Aberdeen eased the pressure on manager Barry Robson with a 3-0 win at Ross County to climb clear of the bottom of the table up to eighth.

Lawrence Shankland scored for the sixth consecutive game as Hearts beat bottom-of-the-table Livingston 2-1 to open up a five-point lead in third.

Hibs needed a stoppage time equaliser from Elie Youan to salvage a 2-2 draw at home to Motherwell.