First-half goals from their captain, Richard Gough, and Paul Gascoigne ensured a fourth victory in less than a fortnight as the champions chase their ninth successive title. Jorg Albertz added a third before Ally McCoist scored Rangers' 50th League goal of the term with a 20-yard strike 10 minutes from time.
Brian Laudrup took the fight to Raith and, in the sixth minute, his cross from the left was headed over the bar by Gascoigne. The Dane sliced open Raith again four minutes later when he set up Charlie Miller, who flicked the ball beyond Scott Thomson, but a linesman's flag cut short the celebrations.
McCoist was the next to go close as he stopped a long-range shot from his team-mate, Ian Ferguson, but stabbed his effort wide of the target. Gascoigne hit the post and then Alex Taylor headed a Gough header off the line onto the bar and out before Raith cracked after 29 minutes. Gough claimed his fifth goal of the season, meeting a Laudrup chip to power his header beyond Thomson.
Gascoigne raced more than half the length of Ibrox to make it 2-0 after 36 minutes as Rangers punished Raith with a swift counter-attack. The Kirkcaldy side had scarcely been able to venture forward but, when Alan McLaren broke down an attack, a flick by McCoist enabled the England midfielder to race clear and drive home his 15th goal of the season.
Two minutes after half-time it was 3-0 as Albertz gleefully blasted home a McCoist cut-back with his left foot. Raith's Alex Taylor collected a yellow card and then missed a great chance to cut the lead as Rangers eased off the pedal. Thomson did well to deny McCoist a goal before Andersen replaced his fellow Dane, Laudrup, with 15 minutes left. Then came McCoist's party-piece. He totally miskicked as Albertz looked for a return pass, then opted to shoot instead and unleashed his 18th goal of the season high above Thomson.
"They are frightening," the Raith manager, Iain Munro, said. "For spells you think you can hold them but then they hit you again. Gascoigne's goal was an example as they took three or four passes to go from one end of the park to the other.
"It could have been any number of goals against any team here. There are better teams than us who have been turned over at Ibrox. We drew 2- 2 with them the last time, but today there was definitely a gulf."
Walter Smith, the Rangers manager, said: "I wanted to get off to a good start and we did that with some good moves and some good goals. Apart from taking the foot off the gas once in a while in home games, I am very pleased. It was a good day's work." Rangers could recall Joachim Bjorklund for tomorrow's visit to Kilmarnock and rest Alan McLaren.