Rangers have a game in hand after their lunchtime game at St Johnstone was called off due to the frost but Celtic can increase the pressure in Govan next week in a game which now takes on added significance.
Celtic manager Tony Mowbray was forced to pair teenagers Josh Thompson and Thomas Rogne at theheart of his defence due to injuries and suspensions.
It was feared they would be a weak link in an already erratic defence but the inexperience duo cruised through the first half, and indeed, most of the game, barely being tested by a strangely lacklustre visiting side.
United had already taken four points from six against Celtic this season and with Scotland boss Craig Levein, their former manager, watching from the stand they must have fancied their chances again against such an inexperienced and unfamiliar Parkhead defence.
Levein, though, watched Keane open the scoring for the home side in the 21st minute after Kamara had cleverly sprung United's offside trap.
From then until the half-time whistle, Celtic dominated with Keane pulling the strings.
In the 33rd minute United defender Garry Kenneth was booked for a cynical foul on Marc-Antoine Fortune just outside the box but again the Taysiders survived the set-piece.
Rogne might have scored his first Celtic goal when he climbed high to meet a Ki Sung-Yueng corner from the right but the Norwegian defender headed past the far post when it looked like he should have hit the target.
Then, in another brief spell of pressure on the United goal which promised a second goal for the Parkhead side, Pernis had a fine block from Scott Brown's thunderous shot, before making another decent save from Fortune moments later.
Aside from an Andy Webster header which flew wide of the target, the Tannadice side had rarely threatened.
United boss Peter Houston would have been looking for a massive improvement from his side after the break.
However, just four minutes in to the second half Celtic wasted another chance to possibly tie up the points when Keane set up Fortune only to watch the former Nancy striker mis-kick from six yards out, with Kenneth gratefully clearing.
As United appeared at last to be getting down to work and go at Celtic, Prince Buaben fired over the bar from 30 yards.
But the Hoops' soon reasserted themselves and Pernis again had to block from Brown after the Celtic captain had been set up by Ki, whose resultant corner was headed straight at the United keeper by Rogne.
A snap-shot by Kamara just before the hour mark drew another decent save from Pernis who, moments later, made an even better parry from Keane.
But Pernis was again called in to action to tip a goal-bound shot from Landry N'Guemo round the post with the visitors again escaping from the corner unscathed.
With only one goal to show for their dominance, there was no hiding the tension which enveloped Celtic Park in the closing stages and there was a collective gasp of relief in the 78th minute when Hoops' keeper Artur Boruc had to make a point-blank save from Jon Daly.
However, Celtic were not further troubled and deservedly took the three points which spices up the title race ahead of next week's trip to Ibrox.