Ally McCoist's side have wrapped up the title with eight games remaining after moving into an unassailable 26-point lead ahead of second-placed Dunfermline.
Victory over the Diamonds confirms Rangers' place in the SPFL Championship next season after they completed the second stage of their journey back to the top of Scottish football in style, with the trophy set to be presented to the Gers when they host Stranraer on the final day of the season.
After their shocking William Hill Scottish Cup display against Albion Rovers on Sunday, McCoist's side made sure they gave a packed Ibrox plenty to cheer as they confirmed their status as third-tier champions and became the first Scottish club to wrap up their title this term.
Lee McCulloch got the party started in front of a 41,343 crowd as he put the hosts ahead from the penalty spot with just two minutes on the clock after former Light Blues keeper Grant Adam brought down the onrushing David Templeton.
Their advantage was doubled shortly afterwards when the skipper made it two from two from twelve yards after Templeton was fouled, and the 35-year-old completed his third hat-trick of the campaign to all but clinch the points that sealed their second consecutive league crown before the first half was out.
The second period was to prove a cruise over the line for the champions as they eased their way to victory and the title, a Bilel Mohsni shot that came back off the far post the nearest they came to adding to their advantage.
The only negatives on the night for boss McCoist were injuries to Templeton and Andy Little, with the pair both pulling up just before the break with injuries and they are now doubts for the meeting with the Pars at Ibrox on Saturday.
Rangers, who started at the bottom of Scottish league football after lapsing into adminitration and then liquidation in 2012, are now only one title win away from the Scottish Premiership and the Gers boss is looking forward to the Championship campaign
He said: "We are absolutely delighted, not only to wrap the title up but with the manner we wrapped it up, particularly in the first half, which was really pleasing and we are thrilled for the players, the staff and the supporters.
"It has been a terrific league campaign and I thought we finished it well.
"I think 26 wins and two draws is a great achievement, the players deserve an enormous amount of credit, as do the supporters.
"These are all championships that we have to win, to get back to where we want to be, in the top flight.
"These are stages in our recovery which must be met so I think it is only fair that they should be celebrated as you would winning any league.
"There are a lot of boys in the dressing room winning their first league, the majority of players will go through their careers and not win a league.
"The Championship could and hopefully will be, a great league next year so we are certainly planning for that and hopefully we strengthen and continue to build for the championship and for the years after that."
McCoist lavished praise on veteran McCulloch, whose hat-trick came from the centre-half position.
The former Rangers striker said: "I actually scored a quicker hat-trick in Vladikavkaz in a Champions League match than the time Lee scored in tonight.
"But I wasn't playing centre-half to be fair. I think the last person to do it here was Paul Gascoigne on the day we won the title against Aberdeen - although I draw the line at saying they were similar players.
"But it's an unbelievable achievement.
"McCulloch epitomises the spirit that has been required within the club at the beginning of the journey back.
"I'm absolutely thrilled for him. For a captain to score a hat-trick from centre-half on a title-winning day is real 'Roy of the Rovers' stuff."