An own goal from Sean Dillon after just nine minutes was just what Walter Smith would have wanted.
And a second-half blitz saw Kenny Miller add two more goals either side of a Steven Naismith header.
The Gers’ gaffer made two changes to the side that earned a creditable draw against Manchester United in midweek.
Nikica Jelavic, ineligible in Europe, and Vladimir Weiss returned to the starting line-up with Kirk Broadfoot and Steven Naismith making way.
The inclusion of both Lee McCulloch and Mo Edu meant that Steven Davis reverted to a right sided role with Weiss, who was named man-of-the-match, filling the left flank.
With the usual back four restored Sasa Papac moved back to left back from the middle, with Steven Whittaker on the opposite wing.
After a 3-1 win against Aberdeen at Tannadice last weekend United came in to this fixture with confidence despite having had an erratic start to the campaign.
And within the first minute Barry Douglas tried his luck with a long range effort but it was straight at McGregor.
At the other end Weiss cut inside from the left flank but his near post shot failed to trouble his Slovakian teammate Pernis.
It was an entertaining start and on nine minutes Rangers were presented with an early gift to break the deadlock.
Davis was found acres of space on the right wing and his low, teasing delivery was smashed in to the net by the unfortunate Dillon.
It was a bizarre own goal from the full-back who was clearly concerned by a late run made by Jelavic in the box.
In the early stages it was clear that Weiss was going to try to enjoy this run-out but on 15 minutes he was booted up in the air by Scott Robertson who had clearly had enough of watching the Slovakian’s tricks and flicks at the corner flag.
The midfielder was booked as a result.
United skipper Jon Daly was then given the second yellow card of the game from Dougie McDonald for a similar assault on Vlad, this time on the half-way line.
The young winger, however, shrugged off both challenges and on 25 minutes he skipped past three defenders before firing a shot across goal which went a foot wide of Pernis’ far post.
The 20-year-old’s skill and pace brought the Ibrox faithful to their feet on more than one occasion but United came back in to this contest and showed just why they were successful in the Scottish Cup last season.
On 27 minutes the lively Goodwillie crossed from the right and Bougherra, who was outstanding throughout, had to glance the ball away nervously with Daly ready to pounce for what would have been a certain goal.
A deep cross from Dixon was then kept in play by Daly and Morgaro Gomis slid in but could not get his shot on target.
After the half hour mark the tempo of the game dropped with McGregor and Pernis not being tested again prior to the interval.
With a narrow lead in place Walter Smith stuck with the same eleven players for the restart and straight away Jelavic tested Pernis with a rasping shot which brought a good save from the keeper.
The Croatian then tried an acrobatic effort from a Steven Whittaker cross but the ball finished in the Copland Road Stand.
United were looking slack and three minutes in to the second period the club’s £4million signing had his third chance.
Whittaker again delivered a superb cross but the big striker, who looked to be blinded by the sun, skewed his header wide.
The visitors were forced in to their first change on 54 minutes with Johnny Russell replacing the injured Barry Douglas and three minutes later they had their best chance of the game.
A poor touch from McCulloch allowed the Tangerines to flood forward and when Scott Robertson crossed Goodwillie had time to take a touch and look up but his curling effort was well held by McGregor.
With the game opening up Whittaker saw an opportunity to drive forward on 61 minutes but when Miller slid a terrific through pass to the right-back his shot with his left foot was poor by his high standards in these situations.
After a tiring shift at Old Trafford on Tuesday it was understandable if a few players looked jaded at times against a United side with no midweek exertions.
Lee McCulloch, however, showed no signs of this when he blasted a shot from 30 yards which stung the hands of Pernis.
On 68 minutes a second goal finally arrived and it was that man Miller who doubled Rangers’ advantage.
Jelavic’s shot-come-cross found the in-form hitman who calmly slotted the ball home with a precise left foot finish.
With three points almost in the bag Steven Naismith replaced Mo Edu and it was the Scotland star that added a third with 76 minutes on the clock.
David Weir crossed from the left after a deep corner had been delivered by Weiss and Naisy was there to head the ball in to the bottom corner of Pernis’ net from eight yards.
United were now dead and buried and with nine minutes left the game was over when Miller scored his eighth of an impressive season.
Jelavic teed up his strike partner with a delightful pass and Kenny rolled the ball coolly in to the net to put a bit of icing on the cake.