Fraser Forster made a brilliant save from Tom Hateley's penalty, awarded for Kelvin Wilson's challenge on Jamie Murphy, just before Gary Hooper converted a Georgios Samaras cross from close range with 11 minutes remaining.
Not for the first time this season, though, the champions ended up struggling to get three points from a match that should have been over by the interval.
Darren Randolph kept Celtic at bay with a series of saves although there were some glaring misses too before Hooper pounced to take Neil Lennon's side into the winter break nine points clear of Inverness at the top of the table.
Elsewhere, Liam Craig grabbed the only goal of the game to hand St Johnstone a 1-0 victory as Dundee's survival hopes were dealt a further blow.
Nearest rivals Ross County's own match fell victim to the weather but the Dens Park side failed to edge closer to the Highland outfit.
Defeat means Dundee have claimed just one point from their last seven matches.
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 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.
St Mirren failed to clinch a second successive victory in the SPL as Cammy Bell helped Kilmarnock earn a hard-fought 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.
There were late chances for Jim Goodwin and David Barron, but the Rugby Park side held out for a point.
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