Match ends, Rangers 4, Dundee 0.
Rangers powered in to Sunday's Scottish Cup semi-final draw with a slick and determined win over Dundee at Ibrox.
Harry Forrester's drive past Scott Bain after 13 seconds, his third in three games, set the tone for Rangers as he pounced on Kevin Holt's dithering.
Dundee fought to stem the tide but fell further behind in 47 minutes when Jason Holt's header ended a well-worked move.
An Andy Halliday free-kick and a Lee Wallace solo run further underlined the dominance of Mark Warburton's team.
Dundee's bid to lift the Scottish Cup for the first time since 1910 was dealt a stunning early blow in the first move of the match.
With Ibrox sizzling with anticipation, Forrester dispossessed Kevin Holt, pushed forward and lashed in a shot to stun Paul Hartley's side.
Thereafter, Championship Rangers rarely took a backward step, playing with an intensity that their Premiership opponents could not match.
Full-back James Tavernier was key to many of their attacking forays. Dundee goalkeeper Scott Bain did well to palm away one of his fizzing drives and, as Rangers' whirlwind start continued, Forrester's cross from the right was headed towards his own goal by Holt but it bobbled on to the post and was cleared.
The Dark Blues skipper Gary Harkins trundled a left-foot shot a fraction wide of Wes Foderingham's post to change, briefly, the momentum, but Rangers looked hungry to kill off the tie.
Dundee defender Darren O'Dea slid in to clear an inviting Kenny Miller cross and Bain showed quick reflexes to turn round a Tavernier free-kick for a corner.
Dundee had a more productive spell around the half-hour mark when Foderingham threw up a hand to knock away Paul McGinn's cross and Hemmings' skill on the left touchline created an opening.
However, Tavernier soon reasserted Rangers' attacking tempo with a mazy run before being blocked by Paul McGowan.
Yet for all Dundee were on the back foot, they could have pulled level just before half time when Harkins' header towards goal landed in Foderingham's arms when Hemmings, on the six-yard line, needed only to glance it either side of the keeper.
Rangers scored within two minutes of the re-start, the result of a beautifully worked five-man move.
On the right, Forrester clipped the ball in to the box where Barrie McKay chested it down for the on-rushing Miller to cross for Holt who nodded it past Bain.
Rob Kiernan produced an important block in the box to deny one-time Rangers youth striker Hemmings from pulling one back with a left-foot shot prior to Rangers scoring their third, a drive by Halliday around the wall from 22 yards.
Dundee peppered Foderingham's goal with long-range shots but it was Rangers who were celebrating once more before the final whistle when Wallace breezed through the dispirited Dark Blues defence to slot calmly past Bain.
Rangers manager Mark Warburton: "We put on a really pleasing performance from the first whistle.
"We set out tempo and intensity and got the early goal.
"But it was all round the park we performed. We were defensively strong. That's seven clean sheets in nine matches.
"A lot is made of our forward play but don't forget that is a tremendous statement by the back five. It was a really good day's work."
Dundee manager Paul Hartley: "I'm extremely disappointed with the manner of the start.
"The last thing we said to them before we went out was make sure you have a good start to the game.
"We were a goal down after 13 seconds and what that does to the home team, it just gives them a massive lift.
"We have got to be honest with ourselves and say Rangers totally deserved to win today and we didn't perform."
- 23HoltSubstituted forLawat 78'minutes
- 15ForresterBooked at 1minsSubstituted forShielsat 73'minutes
- 19McKaySubstituted forClarkat 73'minutes
- 4KonradBooked at 19minsSubstituted forKerrat 68'minutes
- 21O'DeaBooked at 64mins
- 9LoySubstituted forWightonat 55'minutes
- 22Rodríguez Pérez Reverte
- Alan Muir
- Shots on Target
Second Half ends, Rangers 4, Dundee 0.
Attempt missed. Kane Hemmings (Dundee) right footed shot from outside the box is high and wide to the right.
James Tavernier (Rangers) wins a free kick on the right wing.
Foul by Cameron Kerr (Dundee).
Andy Halliday (Rangers) wins a free kick in the attacking half.
Foul by Gary Harkins (Dundee).
Corner, Rangers. Conceded by Nick Ross.
Attempt blocked. Andy Halliday (Rangers) left footed shot from the centre of the box is blocked.
Attempt missed. Paul McGowan (Dundee) right footed shot from the right side of the box is close, but misses to the right.
Attempt saved. Greg Stewart (Dundee) left footed shot from outside the box is saved in the top centre of the goal.
Corner, Dundee. Conceded by Nicky Clark.
Corner, Dundee. Conceded by Nicky Law.
Attempt blocked. Greg Stewart (Dundee) left footed shot from the centre of the box is blocked.
Goal! Rangers 4, Dundee 0. Lee Wallace (Rangers) left footed shot from the centre of the box to the bottom left corner.
Attempt missed. Nick Ross (Dundee) left footed shot from the right side of the box is close, but misses to the right.
Substitution, Rangers. Nicky Law replaces Jason Holt.
Corner, Rangers. Conceded by Paul McGowan.
Attempt missed. Gary Harkins (Dundee) right footed shot from outside the box is just a bit too high from a direct free kick.
Craig Wighton (Dundee) wins a free kick in the defensive half.