A new-look Rangers took command early on and kept it throughout, their continental talent encouragingly prompted by a young Scot, Barry Ferguson, who orchestrated their flowing performance.
After creating their first goal for Andrei Kanchelskis with a probing pass, he had a hand in Giovanni Van Bronckhorst's second on the stroke of half-time. Ferguson's best moment was Rangers' third goal when he released Rod Wallace for his fifth goal since moving from Leeds this summer, including one in every league game.
With St Johnstone tiring in the closing stages, Jorg Albertz made it four from the penalty spot after John McQuillan's careless trip on Van Bronckhorst.
Ferguson threaded a reverse pass beyond a visiting defence searching for offside, and Kanchelskis flew past them to put Rangers ahead after 26 minutes. Rangers doubled their advantage seconds before the break, when Van Bronckhorst scored with a 25-yard curling shot.
After 56 minutes, Ferguson showed poise in central midfield, biding his time before playing Wallace through who rounded goalkeeper Alan Main to score in an empty net. Van Bronckhorst was tripped in the area by John McQuillan after 85 minutes and Albertz strode up to fire in the spot kick for a fourth goal.
Colin Hendry was the surprise omission for Rangers, the Scotland defender forced to settle for being a 73rd-minute substitute because of a lack of match fitness and the form of Craig Moore.
The Rangers coach, Dick Advocaat, did change the team that drew 0-0 in the Uefa Cup action away to PAOK Salonika. Artur Numan being out injured meant a rare start for Tony Vidmar, while Gabriel Amato displaced Ian Ferguson.
St Johnstone were without the suspended George O'Boyle and much hope from the moment Rangers launched their opening attack in the first minute when Van Bronckhorst's lob cleared the bar.
At Dens Park, a penalty in the second minute of injury time saw Dundee to complete a dreadful week for Celtic by stealing a point.
When Craig Burley robbed Jim McInally and put them ahead midway through the second half, Celtic looked to have lifted the gloom after failing to qualify for the Champions' League in Croatia in midweek and the off- pitch rows.
They appeared to be dealing with all Dundee's efforts quite comfortably, but a mistimed tackle by Enrico Annoni on substitute Eddie Annand brought a penalty. Annand duly netted Dundee's first goal in seven-and-a-half hours of Premier League football.Reuse content