Stephen McManus opened the scoring for Celtic
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Celtic overcame a lively challenge from Inverness Caledonian Thistle to extend their lead to move to within two wins of the Scottish Premier League title.
Maciej Zurawski and Shunsuke Nakamura missed early chances for Celtic, while Graham Bayne ought to have done better than head wide for Caley Thistle.
But Stephen McManus rose to head home a Nakamura corner after 35 minutes.
Shaun Maloney ended Inverness hopes with a superb free-kick before Richard Hart fired a reply with seconds left.
John Hartson and Mark Wilson had returned to the Celtic starting line-up in place of Ross Wallace and the injured Roy Keane after being unavailable for selection for the CIS Cup final.
The home side seemed inspired by that Hampden win and an emotional minute's applause in honour of deceased former winger Jimmy Johnstone.
Nakamura and Zurawski both forced saves from Caley Thistle goalkeeper Mark Brown within the opening two minutes.
But the visitors ought to have broken the deadlock soon after when Bayne pounced on a poor backpass from Bobo Balde but headed over goalkeeper Artur Boruc and past the post.
Neil Lennon almost put Celtic ahead with an audacious chip that fell just wide before Gordon Strachan had to re-organise his midfield.
The Celtic boss was forced to replace the injured Stilian Petrov with Stephen Pearson after 28 minutes.
But Celtic continued to press and defender McManus scored his eighth goal of the season when he sent a looping header over Brown and into the net from nine yards.
Hartson missed a great chance to extend the lead after the break, firing the ball wide from six yards following a fine Wilson cross.
Caley Thistle had appeared to miss sick top scorer Craig Dargo and the suspended Ross Tokely, with Dennis Wyness and Stuart McCaffrey having come into the starting line-up, but the visitors grew in confidence after the break.
Boruc was tested by an 18-yard drive from Bayne, Ian Black volleyed wide and Wyness also sent a drive into the arms of the goalkeeper.
McCaffrey missed a great chance of an equaliser when he headed over from Alan Morgan's corner.
But Maloney curled in the free-kick that effectively settled the game after 79 minutes before substitute Dion Dublin sent an effort against the Inverness post.
However, there was still time for Boruc to give Celtic a nervous finish when he allowed Hart's speculative effort to slip under his body.
Celtic: Boruc, Telfer, Balde, McManus, Wilson, Nakamura, Lennon, Petrov (Pearson 29), Maloney, Hartson (Dublin 68), Zurawski (Thompson 82).
Subs Not Used: Marshall, Varga, Wallace, Lawson.
Goals: McManus 35, Maloney 79.
Inverness CT: Brown, Duncan, Dods, McCaffrey, Hart, Munro, Hastings, Bayne (McAllister 79), Morgan, Black (Wilson 71), Wyness.
Subs Not Used: Fraser, Golabek, Keogh, Fox, Parratt.
Booked: Black, Dods.
Goal: Hart 90.
Att: 57,451
Ref: C Richmond