However, the victory, thanks to an 18th minute Chris Sutton header, was enough to stretch Celtic's lead at the top to four points.
The rare appearance of Juninho just before half-time after Alan Thompson suffered an injury at least brought a little sparkle into the Bhoys' play, especially when the Brazilian combined with the talented Aiden McGeady.
For United, who are still without a victory on their travels, it was a valiant effort but the visitors rarely got forward in sufficient numbers to trouble Magnus Hedman in the Celtic goal.
United forced an early corner but it was soon Celtic who were pushing the visitors on to the back foot.
From McGeady's dangerous corner Alan Archibald headed clear at the back post after Hartson connected with a glancing header.
There was more threat from the home side as Sutton's flick released Stilian Petrov but Tony Bullock managed to parry his powerful shot.
Celtic went even closer a minute later. From Sutton's clever pass Petrov's left foot shot from six yards beat Bullock, but Mark Wilson was on the line to clear.
In a rare break for the visitors Mark Kerr's pass found Wilson and the wing-back went past Joos Valgaeren before cutting the ball back to Jim McIntyre, who delayed his shot too long before being crowded out.
McGeady went close with a snap shot before Hartson was fouled by Chris Innes just outside the box. Thompson's free-kick was deflected for a corner but the Celtic breakthrough was not long delayed.
From Thompson's corner Sutton timed his run to perfection and glanced his header at the near post into the top corner.
Bobo Balde nearly added to Celtic's lead shortly after when he was unmarked at the back post but his powerful header was touched over the bar by Bullock.
Collin Samuel failed to give a touch to Kerr's cross before Hartson's first-time volley from Thompson's pass whistled narrowly over.
Celtic nearly scored again just before half time. Hartson held off an Innes challenge and his shot on the turn spun high into the air off Bullock, but the keeper just recovered in time to punch the ball away from the waiting Petrov.
When Thompson limped off, Juninho was soon involved and his skilful play won a corner.
On the stroke of half-time a Wilson free-kick found Innes at the back post but Hedman was able to smother his header.
Celtic went so close to adding to their lead at the start of the second half. Jackie McNamara's cross found Hartson in space but Bullock did well to claw away his header as it bounced up off the turf.
Jason Scotland who had come on at the interval for Samuel released Kerr into the box but Hedman was quick enough off his line to save at his feet.
The Celtic keeper then did well to touch Barry Robson's in-swinging corner over his crossbar as United enjoyed a rare spell of pressure.
Hartson went down in the box after Sutton had dummied Juninho's pass but his claims for a penalty were dismissed.
Kerr could then only shoot weakly into Hedman's arms after Wilson's cross was headed out to him as United chased an equaliser.
Stan Varga delivered a superb 40-yard pass to put Sutton through on goal but though his shot cleared Bullock it also just scraped over the bar.
Bullock did well to keep out Petrov's free-kick before United had a claim for a penalty in injury time. From Wilson's free-kick Hartson did handle the ball in front of substitute Billy Dodds but the referee had already blown for a free-kick against Innes.
Man of the Match: Chris Sutton
The Englishman was a constant threat to the visiting defence and deserved his winning goal.