Anothony Stokes scored two second-half goals to give Celtic victory against 10-man Inverness.
The home side had Greg Tansey controversially ordered off for leading with an arm in an aerial challenge nine minutes before the interval.
With an hour gone, Stokes finished off a neat passing move involving James Forrest and Gary Hooper.
And the striker volleyed in from an acute angle to wrap up the points with his 11th goal of the season.
Celtic move to within nine points of Scottish Premier League leaders Rangers, who host St Johnstone later on Saturday, while the defeat leaves Inverness bottom of the table.
Both defences looked vulnerable in the early stages.
On 12 minutes, Stokes found room after taking a Georgios Samaras flick at the edge of the penalty box but his shot was straight at Caley keeper Ryan Esson.
Soon after, Jonny Hayes gathered a Tansey pass and curled in a low shot that Celtic keeper Fraser Forster pushed away on the stretch.
Inverness defender Josh Meekings then made a good block to prevent Stokes finding the net from eight yards, after Hooper and Forrest had combined well inside the penalty area.
Stokes celebrates his first goal at the Caledonian Stadium
With 36 minutes gone, an evenly contested match swung in favour of the visitors when Tansey was shown a straight red card for leading with an arm as he challenged for a high ball with Samaras.
Referee Stevie O'Reilly indicated the use of an elbow but contact was with the midfielder's hand and was minimal, leaving the home fans outraged by the decision.
Celtic laboured for a long period to break down stubborn Inverness resistance but the visitors made the breakthrough in style on the hour.
Hooper and Forrest exchanged sharp passes on the edge of the penalty box before the former picked out Stokes for a simple finish from close range.
Ten minutes later, Hooper and Forrest again combined to create another opening for the in-form Stokes.
Forrest's shot from 18 yards was blocked and fell to the Irish striker, who crashed a volley across Esson and into the far corner of the net from a tight angle.
Inverness responded with an enterprising run from Hayes but his final shot lacked power, allowing Forster to save comfortably.
With Terry Butcher's depleted side tiring, Celtic substitute Kris Commons was left unmarked to volley over from an Adam Matthews delivery.
Tempers frayed in the closing minutes when Andrew Shinnie flew into a reckless challenge on Celtic replacement Pat McCourt but O'Reilly was lenient on this occasion, choosing to book him.
Inverness CT 01 Esson 03 Tokely 05 Hogg Booked 22 Gillet 26 Meekings 07 Hayes 08 Tansey Dismissed 10 Shinnie Booked 25 Davis 09 Foran Booked (Proctor - 78' ) 15 Tade (Sutherland - 78' ) Substitutes 12 Tuffey 14 Proctor 19 Shinnie 11 Ross 17 Morrison 20 Chippendale 18 Sutherland Celtic 01 Forster 04 El Kaddouri Booked (McCourt - 69' ) 05 Majstorovic Booked 02 Matthews 16 Ledley 33 Kayal Booked 67 Wanyama 09 Samaras (Ki Sung-Yeung - 54' ) 10 Stokes 49 Forrest (Commons - 81' ) 88 Hooper Substitutes 24 Zaluska 44 Fraser 56 Twardzik 18 Ki Sung-Yeung 20 McCourt 46 McGeouch 15 Commons