Hibs had the better of the first half but found Celtic's stand-in goalkeeper Lukasz Zaluska, replacing Artur Boruc who was out due to a family bereavement, in fine form.
Celtic rallied and in the 61st minute, after Anthony Stokes made a high challenge on Aiden McGeady which was judged worthy of a spot-kick by referee Charlie Richmond, Keane slammed the ball confidently past Graham Stack.
It was the Irish striker's 12th goal in 12 games since arriving on loan from Tottenham in January and will increase interim manager Neil Lennon's chances of getting the job on a permanent basis.
With the Leith club in the throes of completing the re-building of their stadium, the backdrop to the game was a demolished east stand.
The threadbare pitch did little to embellish the surroundings but the home side looked in good condition in the early stages.
In the fourth minute Zaluska made a fine save from Ian Murray's header at the expense of a corner, and as the visitors failed to clear their lines properly Hibernian defender Sol Bamba hooked the ball over the bar from six yards.
Moments later the Polish goalkeeper made another good save, this time from Stokes, blocking the Irishman's angled drive after he had raced clear of the Celtic defence.
Celtic retaliated, with Bamba having to make a saving tackle on Marc-Antoine Fortune 10 yards out after the Celtic striker had been set up by McGeady.
In the 12th minute, Lee Naylor's corner from the right was headed back across goal at the far post by Georgios Samaras and Josh Thompson volleyed over.
Then referee Richmond ignored a penalty claim from Keane after he claimed Murray had handled the ball in the box when dispossessing the striker.
Play zipped from end to end with more pace and power than precision.
Hibs had the upper hand but only just, with the battle between Celtic defender Darren O'Dea and Hibs striker Colin Nish symbolising the meaty encounter.
As the game nudged over the half-hour mark Samaras had a 25-yard drive saved with some comfort by Stack.
Stokes had the ball in the Celtic net in the 39th minute but the offside flag was already up.
As Celtic tried to impose themselves on the game Keane mis-kicked from Fortune's cross two minutes from the interval.
Celtic started the second half in seemingly more determined mood and McGeady, who had showed glimpses of skill earlier, cut inside and drove over the bar from 16 yards.
In the 57th minute, as the home side pressed with some purpose, Nish had an effort from 25 yards easily saved by Zaluska, moments before Stack had a similarly comfortable save to make from Fortune at the other end.
However, Celtic took the lead shortly after Hibs defender Steven Thicot was booked for a foul on Samaras 25 yards from goal.
Naylor's left-footed free-kick was pushed away by Stack for another corner but as the home side tried to clear their lines from the set-piece, Stokes raised his foot in challenging McGeady and Richmond pointed to the spot.
Keane stepped up and rifled the penalty to Stack's right-hand side and took the acclaim of the Celtic fans behind the goal.
Hibs staggered for a few moments but almost drew level in the 68th minute when former Hoops star Derek Riordan, who hitherto had been disappointing, sent a shot from 25 yards crashing off the top of the Celtic bar.
Riordan and John Rankin were replaced by Danny Galbraith and Abdessalam Benjelloun as the Leith side tried to get back level.
However, the expected late Hibs onslaught failed to materialise, leaving Celtic to pick up three more SPL points and Lennon to depart with more brownie points.