Michael Mols led the way with two goals in the opening six minutes and further strikes from substitutes Shota Arveladze and Claudio Caniggia added an extra sheen to the scoreline.
It was the perfect response from Alex McLeish and his men after being written off unduly in certain quarters after last week’s 2-2 draw with Dundee and set them up nicely for next week’s trip to Tynecastle.
In his programme notes, McLeish had called on the fans to back the team to the hilt and the noise that greeted the players when they strode out the tunnel was near-deafening as the supporters played their part.
Galvanised by this backing, Rangers could have been four up within the opening 10 minutes.
The Light Blues had scored with less than a minute gone in the previous match with Dundee and should have done the same again here.
Mols fed a pass out wide to Peter Lovenkrands and, when the Dane’s cross was mis-judged by Greg Shields, Ronald de Boer seemed certain to finish from all of eight yards.
The Dutchman’s legendary cool deserted him, however, and he blazed a shot high and wide of the crossbar.
To their credit, the heads never dropped after that miss and four minutes later Mols made amends for his compatriot’s error when Rangers went in front.
Mikel Arteta slipped a pass through to the former Utrecht striker and with a trademark swivel of the hips he made room to crash a shot past Gordon Marshall and in off the post.
The last time these sides met at Ibrox Mols grabbed two in a 6-1 demolition and the Dutchman matched that total after only six minutes this time around.
Barry Ferguson’s long ball was contested by Marshall and de Boer at the edge of the box and when the ball fell to Mols 25 yards out he expertly lobbed the ball into the gaping net.
For a side chasing third place in the league, Kilmarnock could do nothing about the incessant Gers onslaught to the extent they would likely have needed a map and compass just to escape their own half.
It could have been worse for the Ayrshire side, however, with Rangers missing several decent chances to extend their lead and boost their goal difference at the same time.
Mols, chasing a hat-trick, was unable to convert a de Boer cross from close range when the ball seemed to get stuck under his feet before the rampaging Lorenzo Amoruso wasted two free kick opportunities.
Killie seemed to have weathered the storm and were gradually trying to create opportunities of their own as they chase a UEFA Cup spot.
It was Rangers, however, who finished the half stronger and may still rue three good chances that were passed up just before the break.
With almost every player present in the Kilmarnock box, Arteta’s free kick was deflected onto the far post before Ferguson slid two decent chances wide of the post as the Light Blues went up the tunnel at half-time just two goals to the good.
Arveladze replaced Lovenkrands at half-time as Rangers continued to pour relentlessly forward towards Marshall’s goal.
Amoruso headed over from Fernando Ricksen’s corner after the Dutchman’s initial shot was deflected before Arveladze shot over from a good position.
The Georgian was to have better luck moments later, however, when he put Rangers further in front with a stunning strike.
Mols, who led the line superbly all day, found Arveladze with a short pass and the former Ajax man raced to the edge of the box before unleashing a twisting, venomous drive that arced into the top corner.
With the team gaining a much-needed second wind, only two desperate blocks from Marshall denied Mols his hat-trick as Rangers ran riot.
Arteta curled a free kick narrowly over before Stephen Hughes battered the top of the crossbar as the Light Blues continued to dominate proceedings.
Caniggia replaced the tiring Mols on 76 minutes and three minutes later he added to the scoreline, latching onto de Boer’s searching pass, rounding Marshall and slamming the ball gleefully into the net to round off an excellent afternoon’s work from the Light Blues.
RANGERS (4-3-3): 1 Klos; 2 Ricksen, 3 Moore, 4 Amoruso, 5 Numan; 27 Hughes, 23 Arteta, 6 Ferguson; 14 de Boer (McCann 88), 10 Mols (Caniggia 76), 26 Lovenkrands (Arveladze 46)
Subs not used: McGregor, Malcolm
Booked: None
KILMARNOCK (4-4-2): 1 Marshall; 17 Fowler, 4 McLaughlin, 6 Dindeleux, 2 Shields; 20 di Giacomo, 14 Mahood, 15 Canero, 8 Fulton (McDonald 72); 7 McLaren (Locke 46), 25 McSwegan (Boyd 46)
Subs not used: Stewart, Hay
Booked: McLaren (3), Mahood (29), di Giacomo (35), Fowler (75), Shields (77)
Man of the Match: Michael Mols