With half an hour gone of an absorbing first half on Sunday, the Senegalese striker latched on to a Marc-Antoine Fortune pass before curling an unstoppable shot past Dusan Pernis.
Tannadice substitute Jennison Myrie-Williams, on in the 62nd minute for Danny Swanson, was dismissed in controversial circumstances by referee Iain Brines for picking up two bookings.
However, any doubt over the destination of the points ended in the dying seconds when Keane scored from the spot after Pernis had fouled Aiden McGeady as the Hoops' midfielder ran through on goal.
It was Celtic's fifth SPL win in a row since Neil Lennon took over as interim boss and they were cheered off by the travelling fans at the end.
The Parkhead supporters were in fine voice throughout but in the second minute they were almost silenced when United midfielder Swanson drove in to the box and played in David Goodwillie.
The Tannadice striker kept the ball in play on the byline despite the attention of Hoops keeper Artur Boruc, turned and glanced the near post with a shot with the ball travelling across the line and eventually away to safety.
That set the tempo of the game and in the 12th minute, as the home side took their turn again in pressing, it was Celtic defender Glenn Loovens, back in side for the first time since February after recovering from a hamstring injury, who cleared Garry Kenneth's angled shot off the line with Jon Daly ready to pounce.
The match swayed to and fro but defences remained on top.
Hoops stopper Thomas Rogne, also starting for the first time since February following a hamstring injury, was holding the Celtic defence together at times with some well-timed tackles.
The Tayside rearguard looked more capable against Keane and Fortune in the air than on the ground but in the 30th minute Celtic eventually got in behind the United defence and took the lead through Kamara.
The Senegalese striker ran on to a Fortune pass which split the Tannadice rearguard and steadied himself before curling a shot from 14 yards high past Pernis.
As the Taysiders wobbled, Fortune sent a header just past the post before Darren O'Dea had to replace Rogne who limped off with a reoccurrence of his injury.
A minute from the break Kamara came close to grabbing his second when he sidefooted Aiden McGeady's low cross past the far post from just eight yards out.
Celtic finished the first half on top and moments after the break they had the chance for number two when McGeady's driven free-kick from the left found Keane unmarked 14 yards from goal but the Irishman volleyed over.
United fought back and in the 51st minute Goodwillie received a Daly knock down and sent a low shot past Boruc only to see it crash back off the post before it was eventually cleared by Lee Naylor.
Just before the hour mark Loovens signalled to the bench that his hamstring had also gone and he was replaced by former United player Mark Wilson, a natural full-back who had to go in to central defence alongside O'Dea.
But in the 61st minute Kamara had a great chance to score when McGeady set him up with a clever chip but the Hoops striker opted to volley and his almost casual effort from 10 yards out went high over the bar.
With Celtic taking control, United boss Peter Houston introduced Myrie-Williams for Swanson in the 62nd minute but that was to go wrong.
Although the visitors remained on top the match was still in the balance and there was the feeling that at least one more goal would arrive.
That disappeared in the 76th minute when Myrie-Williams, booked just after coming on for a foul on McGeady, was sent off by Iain Brines for a second foul, this time on Landry NGuemo.
It seemed a rather harsh and confusing decision and the game became somewhat ill-tempered but in the dying seconds Pernis conceded a penalty when he brought down McGeady and Keane slotted in number two from the spot.