Gary Hooper's 79th-minute strike saw the hosts to the three points, just moments after Celtic goalkeeper Fraser Forster made a brilliant save from Tom Hateley's penalty, awarded for Kelvin Wilson's challenge on Jamie Murphy.
The Hoops are now on 43 points at the summit, well clear of second-placed Inverness, whose match at Ross County fell victim to a waterlogged pitch.
A Niall McGinn free-kick shortly after half-time spared the blushes of Jamie Langfield as Aberdeen and Dundee United battled out a 2-2 draw at Pittodrie.
The home side had taken an early lead through Scott Vernon, but Gavin Gunning turned home a leveller and Dons goalkeeper Langfield put through his own net to give the Arabs an unexpected half-time lead.
However, top scorer McGinn blasted a free-kick into the top corner to level the scores, and see that both sides began 2013 with a point.
Liam Craig grabbed the only goal of the game to hand St Johnstone a 1-0 victory over Dundee, whose survival hopes were dealt a further blow.
Defeat means Dundee have claimed just one point from their last seven matches.
St Mirren failed to clinch a second successive victory as Cammy Bell helped Kilmarnock earn a hard-fought point in a 1-1 draw at St Mirren Park.
Liam Kelly fired Kilmarnock ahead from the penalty spot after just four minutes when James Dayton was brought down inside the box.
St Mirren pushed for an equaliser and Bell made three fantastic saves before finally conceding to Paul McGowan's penalty midway through the second half.