Fourth-placed Motherwell were on the fringes of the title race themselves prior to last weekend's defeat at Dundee and dominated Celtic when the sides last met in December.
The visitors were on course for back-to-back wins over the Scottish champions when Elijah Just fired in after Reo Hatate had been robbed at the edge of his own box on 32 minutes.
However, the roles were reversed just six minutes later when Celtic this time won possession inside the Motherwell box and Yang Hyun-jun slotted in an equaliser.
The decisive moment came 19 minutes from time when Emmanuel Longelo was adjudged to have pulled down Daizen Maeda from a corner.
A VAR intervention saw a penalty awarded and a red card shown to Longelo.
Tomas Cvancara, who scored the winning penalty to beat Rangers in a bad-tempered Old Firm showdown last weekend, coolly converted from the spot.
Yang then raced through to fire home his second of the afternoon and seal a vital three points for Martin O'Neill's men.
Rangers are now four points behind their Glasgow rivals ahead of Sunday's trip to St. Mirren.