Ten-man Celtic maintain 14-point lead in Scotland
Leigh Griffiths scored on the stroke of half-time before Callum McGregor saw red a minute after the interval for his second bookable offence.
Despite their numerical disadvantage, Stuart Armstrong added to Celtic's tally before substitute Moussa Dembele sealed their 13th win in a row.
"We were presented with a challenge going down to 10 men for the first time this season, which I thought was an awful decision by the referee," said Celtic manager Brendan Rodgers.
"The kid is hugely disappointed, but there's no fault of his on that one."
Fierce rivals Rangers carved out a narrow 1-0 win over Inverness Caledonian Thistle at Ibrox to strengthen their grip on second place.Â
Mark Warburton's side moved seven points clear of Aberdeen, who won 3-1 away to Motherwell on Friday.
Brad McKay's first-half own goal was enough for Rangers to win a fourth successive game for the first time this season.
"The players have had a bad day in terms of quality of performance, but they've emerged with the three points," said Rangers manager Warburton.
"All credit to them. If you can have an off day and still emerge with the spoils, it speaks volumes for the team."
After grabbing a double in last week's win at Hamilton, Martyn Waghorn retained his place in the Rangers starting line-up and missed an early chance to give his side the lead.
The striker latched onto Joe Garner's headed flick-on and burst into the box from the right, but blazed his effort high and wide.
- Garner goes close -
Lee Wallace's deflected cross then fell to Jason Holt, who tested Owain Fon Williams with an acrobatic bicycle kick.
Despite their early pressure, Rangers almost went behind in the 12th minute when Losana Doumbouya got in front of the Gers centre-back to prod a lofted ball into the box towards goal.
But Wes Foderingham produced a fine save to stop it on the line.
Inverness were to rue that missed opportunity a minute later as Rangers took the lead.
Waghorn beat his man to cut into the box and his fiercely struck cross-cum-shot smacked off McKay and into his own net.
Inverness were unperturbed by going behind and Foderingham came to the rescue for Rangers again as he thwarted Larnell Cole after the Inverness forward intercepted Andy Halliday's slack pass.
Halliday nearly made amends when his vicious 25-yard strike looked to be sailing into the top corner, only for Fon Williams to get a fingertip to it to turn it over.
Foderingham was at full-stretch to turn away a Greg Tansey angled drive before he spilled Lee Hodson's headed back-pass into the path of Liam Polworth, who put his effort off-target.
Rangers' fans have failed in their bid to get The Dave Clark Five song 'Glad All Over' to Christmas number one in tribute to cult hero Garner, whose praises they sing to that tune.
The striker almost gave them something else to sing about in the second half when substitute Kenny Miller's deflected shot was flicked up into his path, but he sent his effort narrowly wide.
Aaron Doran replaced the injured Iain Vigurs for Inverness and the midfielder had a chance immediately, but pulled his shot on the turn over the bar.