Goals from defender Charlie Mulgrew and midfielder Kris Commons, his first of the season, gave the rampant champions a commanding interval lead at Parkhead.
Striker Gary Hooper scored with a thumping drive soon after the break and it looked for a spell as if the home side were going to hand out a real hammering to the Govan men.
However, three goals were enough for the celebrating Celtic fans who can brag of a 21-point lead over their old rivals, an indication of their superiority this season, even in light of the 10 points Rangers were deducted in February for entering administration.
Celtic showed the strength of their squad by bringing back five of their star players.
Goalkeeper Fraser Forster, right-back Adam Matthews, stopper Glenn Loovens, skipper Scott Brown and striker Georgios Samaras all returned for the last Glasgow derby of the season. Out went Thomas Rogne, Ki Sung-yueng, Pawel Brozek, Lukasz Zaluska and Cha Du-ri, the latter two starting on the bench along with 18-year-old striker Tony Watt, who scored two goals on his debut at Motherwell last week.
Gers boss Ally McCoist named the same side which beat Hearts last week with Lee McCulloch leading the line.
It was a peculiar build-up to the game due to Celtic having wrapped up the title last month and the problems of the Ibrox club who are fighting for their very survival, amid a seemingly endless search to find a buyer.
But as Hoops boss Neil Lennon took his seat in the stand - he was serving the second of a two-match touchline ban for criticising referee Willie Collum following the Scottish Communities League Cup final defeat to Kilmarnock in March - the fans were in full voice.
Rangers looked decent enough in the early stages and in the 16th minute they missed a good chance when midfielder Rhys McCabe robbed Brown in the middle of the park with a crunching tackle.
He fed Steven Whittaker who in turned played in Andrew Little but the Gers striker failed to connect properly with his angled-shot from 14 yards and Forster saved comfortably.
A minute later Celtic were ahead through Mulgrew with their first corner of the match.
Commons' cross from the right missed the mass of bodies in the middle to find the unmarked Celtic defender rushing in to bullet a header past Allan McGregor.
The Ibrox defence had to hold firm as the home side went looking for the second, trying to stretch Rangers down the flanks through Emilio Izaguirre and Matthews.
However, their task became even more difficult just after the half-hour mark when Celtic went two ahead through Commons.
Brown's pass to Hooper was quickly moved infield to the Scotland international who took advantage of Rangers defender Kyle Bartley's missed tackle to go through on goal and delightfully chip the ball over the advancing McGregor.
The Ibrox side looked close to unravelling amid the din from the home fans. Celtic midfielder Joe Ledley got on the end of a Commons cross to head wide of the back post before McGregor made a great save from Hoops defender Victor Wanyama, whose drive from the edge of the box looked goalbound and it was a bedraggled looking Rangers who welcomed the half-time whistle.
Damage limitation may have been theme of McCoist's half-time team talk and certainly the early stages of the second half did little to suggest a comeback was on the cards.
Celtic were quicker and sharper, switching play from left to right with ease and no little confidence and in the 51st minute the tireless Izaguirre's lofted cross from the left just avoided Hooper, two yards from goal.
A minute later Rangers had to thank McGregor for a brilliant save from Ledley's dipping volley from 20 yards, and the keeper made another block from Wanyama following the subsequent corner.
However, it merely delayed Celtic's third which came in the 53rd minute when Samaras played in Hooper and he hammered the ball high past the helpless Scotland number one.
As the Light Blues fans sang non-stop in defiance, certain in their side's defeat, Celtic took a breather but remained well in control.
In the 73rd minute Rangers substitute Salim Kerkar, on for Little, had half a chance when the ball broke kindly for him in a challenge with Wanyama but his chip from a tight angle sailed over.
Two minutes later Bartley, suffering a wretched afternoon, was booked for a foul on Izaguirre on the touchline which had the home fans on their feet in understandable anger.
With seven minutes remaining and the game petering out, Forster made a decent save from Sone Aluko's free-kick at the expense of a corner which came to nothing.
Brown picked up a yellow card for a foul on Kerkar near the end but that did not detract from a convincing Celtic win.