Goals by Scott Sinclair, Leigh Griffiths and Rogic ensured Celtic exacted revenge for Inverness
In-form Australian international Tom Rogic scored as Celtic increased their lead at the top of the Scottish Premiership to 10 points with a 3-0 win at home to 10-man Inverness Caledonian Thistle.
Goals by Scott Sinclair, Leigh Griffiths and Rogic ensured Celtic exacted revenge for Inverness being the only side to take points off them this season -- a 2-2 draw in September.
Celtic are 10 points clear of Aberdeen -- who beat Partick Thistle 2-1 on Friday -- with a game in hand, although bitter rivals Rangers could close to within nine points if they beat Ross County away on Sunday.
Celtic boss Brendan Rodgers was delighted with victory after a tough run of games.
"Inverness are a difficult team to play against and our game plan was disrupted," said Rodgers.
"We adjusted it at half time and, within a matter of minutes, we scored the goal and, from there, we were dominant in the second half.
"It was very pleasing after four games when we have been travelling."
Inverness manager Richie Foran was disappointed in his side's display.
"I think we were nervy, we weren't brave enough, we didn't believe and we never expressed ourselves," Foran said.
"I'm a little bit disappointed in their performance but maybe even one of our better performances might not have been good enough for Celtic today."
After a frustrating first half in which they lost defender Mikael Lustig to injury, the champions seized control in the second period.
A 48th-minute strike from Sinclair set them on their way before Griffiths added a second in the 63rd minute with Greg Tansey seeing red for a second bookable foul in the build-up.
Rogic then fired home a third in the 83rd minute.
Lustig's early departure seemed to disrupt Celtic's flow and allowed Inverness a brief respite.
However, the hosts soon recovered their composure and only a fine one-handed save from Owain Fon Williams stopped a vicious volley from Griffiths bursting the net.
The second half was barely two minutes old when Celtic made the breakthrough.
Scott Brown, who this week returned to the Scotland squad after retiring from international football earlier this year, slid a pass to Callum McGregor.
He passed to Sinclair with the English winger applying the finishing touch to send a low shot bouncing under Fon Williams from close range.
Celtic soon built on their advantage as Griffiths, who bagged 40 goals last season, took advantage of a starting opportunity alongside Moussa Dembele to grab his first strike since September 24.
Referee Crawford Allan played the advantage after McGregor was brought down by Tansey, allowing Dembele to test Fon Williams with a curling strike.
The 'keeper got down low to make the save but the loose ball fell to Griffiths who buried it into the net from a couple of yards out.
Tansey's challenge on McGregor in the build-up was to prove a costly one for Inverness as the defender was shown a red card after picking up his second booking.
Celtic cut through the 10 men of Inverness at ease as they made their extra man count and Rogic completed the scoring late on.
The substitute got on the end of Stuart Armstrong's cut-back to the penalty spot and his left-foot strike flew into the net via a slight deflection off an Inverness defender on the line.
Elsewhere, Hearts move up to third with a 2-2 draw with St Johnstone and Dundee move off the bottom with a 2-0 win over Motherwell.