It was a dominant win on an afternoon of positives as Steven Naismith hit double figures for the season and Jelavic’s treble setting him on Naisy’s tail in the goal hunt.
The introductions of Kyle Bartley and Healy to the top team were a welcome bonus for Walter Smith, whose only negative will be the loss of Naismith in the first period to what looked like a tightening of the hamstring.
Rangers could barely have been less troubled in the opening 45 minutes with signs positive for the Light Blues from the opening minute.
While Bartley was the talk of the stadium ahead of kick off it was fellow January signing Diouf who almost got the home side off to the perfect start.
He latched on to Weiss’s through ball and beat the three man central defence only to poke his left foot effort wide of the upright.
Light Blues fans didn’t have long to wait to celebrate the opener though, with Weiss again the creator.
His delivered from the left and Naismith produced another of his perfectly timed runs to elude the defence and slip his chance inside the near post.
The goal seemed to knock the stuffing out of Stuart McCall’s side and they barely threatened Allan McGregor’s half, let alone his goal for the first half hour.
However Walter Smith’s men couldn’t add to their score and they were served a warning just after the half hour when a series of well delivered crosses caused some concern in the home box.
Tom Hateley struck two dangerous free kicks before Gavin Gunning whipped a wicked cross in for John Sutton to head narrowly over.
The Gers heeded their warning though and within five minutes were three ahead.
And it was Nikica Jelavic who was the clinical finisher, notching both with his right foot.
The first came as the final part of a three touch move that saw Bartley release Steven Whittaker on the right, with the full back rolling the ball across first time for Jelavic to fire home without breaking his stride.
And the second on 36 minutes was a perfect opportunist’s strike with Weiss spotting the Croatian’s movement and picking him out with a free kick from the right.
Jelavic stole a march on the visitors’ defence and hooked his effort home from just inside the six yard box.
He almost completed a hat trick before the interval when he met a John Fleck delivery from the right but couldn’t control his effort on target.
It was a fine introduction for Fleck who had replaced Naismith minutes before the break with the Scotland international seemingly suffering a tightening of his hamstring again.
The second period had a hint of the training game around it despite some contentious moments and one wonderful save from McGregor.
The Scotland No.1 pulled off another brilliant fingertip save to deny sub Ross Forbes whose long range effort looked bound for the back of the net.
A few minutes later Madjid Bougherra was bizarrely booked by referee Alan Muir for a quickly taken free kick before the whistler frustrated the home support by keeping his card in his pocket when Forbes aimed a kick at Weiss.
The Motherwell midfielder was booked on the hour mark for a tug on Weiss as the frustration set in among the visiting players.
It was little wonder as they were experiencing little joy in working their way back in to the game and with the contest effectively over Smith took the chance to make further changes.
Mo Edu was introduced for Bartley who left to a warm reception, but not before Healy’s introduction almost took the roof off Ibrox.
He replaced Diouf and was desperate to make a quick impact. Paired with Jelavic on the hunt for a hat-trick they were two players not keen for the game to end.
And though credited with his treble by the Ibrox tannoy announcer it was in fact visiting defender Shaun Hutchison who turned the fourth in to his own net.
He was on the end of Fleck’s cross after a great break from Steven Davis.
The Croatian wasn’t to be denied however and just moments later he produced another fine right foot finish to complete his first hat-trick for the Light Blues.
Healy wasn’t to be outdone by his strike partner though and when the chance was presented to him he didn’t pass it up.
He latched on to a loose ball in the box and rolled it under Randolph to round off a brilliant afternoon’s work for the home side and secure a memory he’s never likely to forget.