It was a hard-fought win for Neil Lennon's side who once again had to come back from conceding an early goal when Well striker Michael Higdon headed the home side into the lead in the 11th minute from a Tom Hateley cross.
However, three minutes later Celtic were level when Anthony Stokes volleyed in at the back post after Georgios Samaras flicked on a Kris Commons' corner.
Hooper replaced Commons after the break and in the 79th minute he was on hand to tap in a Stokes cut-back from close range before Well defender Tim Clancy was handed a straight red for kicking out at Hooper.
Celtic, who are now 12 points behind Rangers, have a game in hand over their fierce rivals and by the way their fans celebrated at the end there is still genuine belief the champions can be caught although the Hoops boss will want some easier afternoons on the way.
Lennon made two changes to his side for the keenly-awaited trip to Lanarkshire, one enforced.
Thomas Rogne replaced the injured Glenn Loovens at the heart of the Celtic defence while midfielder Commons came in for Paddy McCourt who dropped to the bench.
Well defender Stevie Hammell passed a late fitness test on his ankle knock while midfielder Steve Jennings, who had recovered from a back injury, came in for Shaun Hutchinson who started as substitute.
Lennon's side went into the game with confidence after beating Rennes 3-1 in the Europa League at Celtic Park on Thursday night.
But it was the visitors who had to withstand a series of Hateley early corners as Stuart McCall's men pressed for the opener.
And it was in the 11th minute, from a short corner taken with Nicky Law, that Hateley crossed into the box for the burly Higdon to glance a header past Fraser Forster from six yards out.
It was an all-too familiar lapse in concentration from the Hoops defence who looked around in wonderment.
However, three minute later the Parkhead men were level when a Commons corner from the left was helped on by striker Samaras and Stokes was at the back post to volley past Well keeper Darren Randolph.
The match was living up to its promise as Celtic began to dominate possession.
In the 25th minute Samaras had a chance when Commons' driven free-kick from 30 yards ricocheted to his feet eight yards out but his shot was deflected past for corner from which Rogne's header at the back post was blocked.
After Motherwell midfielder Keith Lasley picked up a booking for catching Hoops skipper Beram Kayal, Higdon had a poorly-struck drive from 12 yards easily scooped up by Forster after Jamie Murphy had fed the ball into the box.
In the 36th minute Well skipper Stephen Craigan headed a Hateley corner high and wide but by this time the early ferocity had subsided.
It was all to play for at the start of the second half which began with Celtic looking the more determined.
In the 49th minute a long punt from Celtic stopper Daniel Majstorovic saw Stokes racing past Craigan and into the box but the former Hibernian striker appeared to be caught just a little by the Fir Park veteran and was off-balance as his shot was blocked by Randolph.
Three minutes later Stokes picked up a booking for dissent by Charlie Richmond after being penalised for tangling with Clancy as he tried to go past the Well defender down the line.
It looked like the Celtic player had just cause for his grievance but as the tempo was cranked up again, Commons was denied by a robust penalty-box tackle by Jennings.
At the other end Forster had to rush from his line to block Law who had moved on to a clever lobbed pass from Lasley at the edge of the box.
Hooper replaced Commons in the 58th minute and he teamed up with Stokes in attack for a combination that would later prove lethal.
In the 76th minute Stuart Carswell replaced Jennings while McCourt came on for Samaras and play continued to rage from end to end, uncontrollably at times.
But with time running out, McCourt dribbled to the edge of the Motherwell box and played in Stokes who drove the ball across goal for Hooper to knock in from almost on the line.
In the 82nd minute Clancy was sent off after appearing to kick out at Hooper and with it went any real chance of a Well comeback, although the same cannot be said of Celtic's title hopes.