0818 GMT April 21, 2018
Scott Sinclair put the visitor on its way from the penalty spot on seven minutes after Patrick Roberts was tripped by Myles Beerman's reckless challenge, skysports.com reported.
Leigh Griffiths doubled Celtic's lead before halftime and three goals after the break by Callum McGregor (52), Dedryck Boyata (61) and Mikael Lustig (87) completed its scoring.
Kenny Miller, who signed a one-year contract extension with Rangers on Friday, netted a consolation for the host (81).
Celtic dominated throughout at the home of its fierce rival and is now five matches away from ending the domestic campaign without defeat.
The champion, which beat Rangers 2-0 in their Scottish Cup semifinal last Sunday, has won five of the six Old Firm meetings this season.
Brendan Rodgers made one change from the semifinal victory as Griffiths replaced Moussa Dembele, who suffered a hamstring injury at Hampden.
And the visitor controlled the game from the off, going close through McGregor before a rash Beerman tackle handed Sinclair the chance to open the scoring.
The winger made no mistake with his spot-kick, sending Wes Foderingham the wrong way for his 21st league goal of the season.
He could have had a hat-trick in the first half as he squandered two more golden opportunities.
The first came after Griffiths struck the crossbar but Sinclair dragged his follow-up wide, and the second saw the former Man City winger badly miscue when unmarked at the back post.
By that stage, Celtic already had a two-goal cushion thanks to Griffiths' superb strike.
Stuart Armstrong set the forward away down the left channel and his left-footed blast beat Foderingham to the top corner.
That momentum continued into the second half as the visitor made it three seven minutes after the break.
Roberts teed up McGregor, who took a touch before firing low through the legs of James Tavernier and into the far corner.
Boyata headed home his third league goal of the season as Celtic punished poor Rangers marking and hesitant goalkeeping to further stretch its advantage.
Martyn Waghorn spurned a glorious opportunity to pull one back before Old Firm stalwart Miller restored a modicum of pride for the host.
But there was more pain to come as Lustig danced past Danny Wilson to curl in Celtic's fifth.