Despite the draw Celtic returned to the top on goal difference from Hibernian ahead of their crucial Champions League clash against Barcelona at Parkhead on Wednesday.
Neil Lennon felt his side didn't get the result they deserved.
"It was very frustrating because we were brilliant today," the Celtic manager said.
"We dominated the game and we got the two goals which we thoroughly deserved and then we didn't deal with a couple of balls into our box.
"I just think we were unfortunate today. I don't think anyone could take away from the fact we were excellent."
His United counterpart had a different view.
"I think we were well worth the result if you look at the game. We put a lot of work into the game," Peter Houston said.
"Great credit to our players today - they showed the character that I know they've got. Our form hasn't been brilliant but that result today could maybe kick-start our season.
Celtic started on the front foot and Adam Matthews and Scott Brown combined to send Commons scampering into the box but sent his shot straight to Radoslaw Cierzniak.
Charlie Mulgrew picked out Brown with a deep cross from the left but the Celtic captain arrowed his header wide from six yards.
Celtic had a chance straight from kick-off in the second half when Tony Watt slipped a pass through for Emilio Izaguirre but the left-back blasted his shot wide of the near post before falling on the turf.
The Honduran international needed treatment following the fall and eventually trudged off to be replaced by Miku.
Dundee United were next to miss a golden chance to take the lead in the 50th minute.
John Rankin teed up Willo Flood for a powerful drive that Fraser Forster could only parry into the path of Johnny Russell but, with the goal gaping, the striker blazed his strike over the bar from 10 yards.
In a period of sustained pressure from United they came close again in the 58th minute when Douglas sent a superb ball into the six-yard box from a free-kick but Gavin Gunning failed to connect properly with the ball and stabbed it wide.
However, after weathering the storm it was Celtic who made the breakthrough in the 69th minute. Miku received a flick on from Watt and the Venezuelan took two touches to set himself up before he lifted the ball high over Cierzniak and into the net.
Watt doubled Celtic's advantage in the 80th minute when a terrible goal kick from Cierzniak landed at his feet and he drove at Rankin before unleashing an unstoppable shot low past the keeper.
Gary Mackay-Steven gave United some hope late on when he guided a shot beyond Forster in the 89th minute after Rudi Skacel's initial effort was blocked.
The home side pushed forward for an equaliser and after Russell had stabbed a shot wide United grabbed an equaliser when sub Ambrose sent a looping header over his own keeper and into the net after connecting with a dangerous cross from Barry Douglas.
Source: AFP
Source: AFP