Hoops keeper Fraser Forster made a brilliant save from Tom Hateley's penalty, awarded for Kelvin Wilson's challenge on Jamie Murphy, just before Hooper converted a Georgios Samaras cross from close range on 79 minutes.
Well keeper Darren Randolph kept Celtic at bay with a series of saves although there were some glaring misses too before Hooper pounced to take Neil Lennon's side into the winter break nine points clear of Inverness.
Samaras had the ball in the net from Kris Commons' cross in the second minute but was flagged offside. Commons then flashed a shot from the edge of the box just wide after being set up by Hooper.
In the seventh minute Darren Randolph made a fine save from Hooper's stab from close range after more good work on the left from Samaras, before tipping stand-in skipper Charlie Mulgrew's curling free-kick over the bar.
There was no let-up in the pressure on the Motherwell goal and moments later Randolph flew to his left to pluck a goal-bound Commons shot out of the air.
Jamie Murphy, skipper for the day on his farewell appearance ahead of a move to Sheffield United, should have put the visitors ahead following a break in the 20th minute when he was played in by Keith Lasley but he lashed the ball over the bar.
In the 37th minute Murphy tested Forster with a drive from the edge of the box and moments later curled a shot from 14 yards past the far post.
With seconds remaining Efe Ambrose missed the chance of the half when Randolph dropped Wanyama's header from a Mulgrew corner, the Parkhead defender hooking the ball over the bar from barely two yards.
Celtic had an unconvincing start to the second period but with six minutes gone Randolph tipped a deflected shot from Wanyama over the bar.
Motherwell were handed a great chance to take the lead when referee Steven McLean adjudged Wilson to have tripped Murphy in the box. There was some concern as to whether Hateley had the ball on the spot or not - and Forster was booked for pointing this out - but when the Motherwell player blasted his shot to his left the Celtic flew across to make a great save.
The incident seemed to energise Celtic and they were soon in the lead when Hooper played the ball to Samaras and ran into the box to collect the return pass and slip the ball under Randolph from six yards.
There were some nervy moments before the final whistle as Motherwell went for broke but in the end Celtic deserved their win.