After seeing off the Jambos 3-0 in their League Cup semi-final last weekend, Celtic continued their stunning return to form after a difficult start to the campaign with a sixth straight win in domestic competitions.
French striker Odsonne Edouard scored twice to take his tally for the season to 11, while on-loan Leicester defender Filip Benkovic scored his first goal for the club to give the hosts a commanding 3-0 half-time lead.
James Forrest and a Ryan Christie penalty rounded off the scoring as Brendan Rodgers's men have now scored 20 goals in their last four league games after hitting just seven in their first seven of the season.
Rangers remain just four points back of their Glasgow rivals as Steven Gerrard's side scored twice in the final 10 minutes in a 2-0 win to condemn St Mirren to a seventh straight defeat.
Daniel Candeias opened the scoring with what appeared to be an attempted cross, but after the disappointment of losing to Aberdeen in the League Cup semi-finals and being held by Kilmarnock in midweek, Gerrard insisted that was a break his side deserved.
"Sometimes you need a little bit of luck to get that breakthrough as we were relentless in trying to find it," said the former Liverpool captain.
Alfredo Morelos then sealed the points in stoppage time.
"The pleasing thing for me is that we didn't hang on, we went and built on that and went and finished the game off," added Gerrard.
"Even though we have had a difficult week, or a frustrating week as I should put it, it is not through lack of trying, we have played well within the games, we just haven't had that run of the ball or had that that quality to break sides down."
Victory moved Rangers into third, ahead of Kilmarnock, who host Aberdeen on Sunday.
A tumultuous week for Hibernian boss Neil Lennon ended in another disappointment as the Edinburgh side were beaten 1-0 by Joe Shaughnessy's late header for St Johnstone.
Lennon was hit by coin in a bad-tempered 0-0 derby draw with Hearts in midweek and believes he has consistently been the target of anti-Irish racism during his time in Scotland, firstly as a player and manager of Celtic and now in the capital.
At the other end of the table Dundee were beaten for the 10th time in 11 league games this season 1-0 at Motherwell, while 10-man Hamilton also beat Livingston 1-0.