Dean Shiels races in to congratulate Nicky Clark on opening the scoring
Rangers swept Airdrieonians out of the Scottish League Cup with a dynamic and assured display that left the League One side reeling.
Before Airdrie had even found their bearings in the game, they were three goals behind and the tie was lost.
Nicky Clark opened the scoring after just four minutes, before Andy Halliday and Martyn Waghorn struck.
Airdrie regrouped after the interval, but Dean Shiels and James Tavernier added goals for ruthless Rangers.
The contest was never evenly-matched, since Rangers kept the ball with crisp, short passing right from the kick-off, which left the home side unable to settle.
They were moved around into a state of disarray, and when they conceded a free-kick on the right, Halliday swung the ball towards the near post and Clark was sharpest to react, stabbing the ball past the Airdrie goalkeeper Neil Parry.
Gideon Zelalem, making his debut following a loan move from Arsenal, was prominent early on. The midfielder was assured with the ball at his feet and displayed a good range of passing.
With Rangers constantly looking to move the ball from one flank to the other, the Airdrie players were pulled out of position, and alarm spread.
Another series of passes carried the ball down Rangers' right flank before it was moved infield to Zelalam. He slipped it to Halliday, who rifled a shot into the corner of the net from 25 yards. Airdrie were stunned, and the visitors were in the mood to be ruthless.
Airdrieonians' Jamie Bain tussles with Barrie McKay
Seconds later, Zelalam swept the ball from left to right for Waghorn, who bustled into the area before sliding a shot inside the post and Parry. At that stage, after just 15 minutes, the question was by how many goals Rangers would secure their passage into the next round.
Waghorn skewed an effort wide, and Nathan Oduwa's creative effort from the corner of the box was saved by Parry. The Airdrie supporters did not lose their black humour, though, and their biggest cheer of the opening half came when the home side won a free-kick.
Some of the intensity slipped from Rangers' play after the break. Oduwa continued to threaten with his feints, jinks and step overs.
The tricks were eye-catching, but the technique and work rate of Halliday carried greater substance. Playing in the holding role, he was the visitors' most influential player, and delivered a series of cross-field passes that were expertly weighted.
He also rattled the crossbar with another long-range effort, with the ball almost bouncing in off the back of Parry, who was left floundering. Airdrie were more bullish themselves in the second half, with Prunty lifting one shot over and Alan Lithgow volleying Nicolas Sumsky's corner wide.
They were only brief flourishes of resistance, though, and Rangers eventually added a fourth. Oduwa sent the rejuvenated Lee Wallace down the left and his cutback was struck on target by Shiels. Parry blocked, but Shiels reacted first to lift the rebound high into the net.
The Airdrie players were drained and dispirited, and they had no answer to Tavernier's desire to leave his stamp on the game. The full-back surged infield, slalomed past several chances as he darted into the penalty area, then he lashed the ball beyond the exposed Parry.
The final score line reflected Rangers' dominance, but also their attacking intent.