Michael Higdon headed Motherwell into an 11th-minute lead but Anthony Stokes replied from close range soon after.
With 10 minutes remaining, Hooper finished off a fine move involving Paddy McCourt and Stokes.
Motherwell's hopes of a comeback were dented when Tim Clancy was sent off for a foolish kick at Hooper.
The victory for Neil Lennon's team edges them ahead of Motherwell on goal difference, 12 points behind leaders Rangers, although they have a game in hand on both rivals.
Having weathered an early storm from the Steelmen, Celtic dug in and ground out a crucial result to relieve some of the pressure on Lennon.
Motherwell made all of the running in the opening exchanges, winning a series of corners against an uncertain Celtic defence.
And from the fifth of those set-pieces, Celtic were caught napping, allowing Tom Hateley to work a short pass with Nicky Law before swinging in a cross for Higdon to glance home from close range.
However, Celtic replied immediately with Stokes equalising from their first corner.
Georgios Samaras rose impressively to nod a Kris Commons delivery towards the back post and up popped the unmarked Irish striker to volley into the net.
Following the flurry of goalmouth incidents, the flow of the match deteriorated, with play disrupted by several robust midfield challenges from the home side.
Celtic defender Thomas Rogne saw his header from corner blocked on the goal-line by Keith Lasley but there was no further threat to either goalkeeper in the first half
Higdon managed to connect with low cross from Jamie Murphy but the striker's shot was tame, allowing Fraser Forster to gather comfortably.
The second half was four minutes old when Stokes raced on to a simple, long ball but Well keeper Darren Randolph was out quickly to block the shot.
Stokes set up Commons moment later and the midfielder, making his first start since his ordering off at Hearts on 2 October, did well to skip by one challenge in the penalty area but his progress was halted by a Steve Jennings tackle.
Motherwell broke swiftly and a lofted pass from Lasley fell for Law, only for Forster to use his large frame to close down the former Rotherham midfielder.
On 65 minutes, Murphy broke into the Celtic penalty area from the left and did well to thread a pass into the six yard box but Forster was alert and got a glove on the ball to deny Higdon a shooting opportunity.
Soon after, Murphy once again found the ball at his feet close to the Celtic goal but was crowded out by a cluster of green and white shirts as he shaped to shoot.
The winning goal came on 80 minutes, with substitute McCourt waltzing his way from the halfway line to the edge of the penalty box before feeding Stokes on the left and the striker's low cross was diverted home by Hooper.
Motherwell's day got worse when Clancy was sent off for a petulant kick at Hooper and Celtic held on to their lead with ease.