Rangers suffered another post-international break slump when they were held to a goalless draw by St Johnstone at Ibrox.
Neither side were able to find the back of the net, with the stalemate allowing Celtic to close the gap on the SPL leaders to 10 points following their 2-0 win at Inverness Caledonian Thistle.
Anthony Stokes' second-half double gave Celtic victory after midfielder Greg Tansey had been sent off for the home side in the 36th minute.
Motherwell strengthened their grip on third place with a 2-1 victory over Aberdeen.
Omar Daley marked his first Motherwell start with the winner, firing home from 18 yards in the 53rd minute.
Scott Vernon had earlier levelled for the Dons after Michael Higdon headed the visitors in front, but Aberdeen rarely looked like equalising again.
First-half goals from Kenny McLean and Nigel Hasselbaink helped St Mirren to a 2-1 victory over Dunfermline at St Mirren Park.
Pars midfielder Joe Cardle pulled one back after 63 minutes to set up a nervous finish, but Danny Lennon's men held out for the three points their play deserved.
Manuel Pascali put the visitors in front after 36 minutes before half-time substitute Leigh Griffiths equalised after 50 minutes to earn Hibs a point.