Dundee United gave boss Jackie McNamara victory in his debut match as Rangers' defensive frailties were punished in the fifth round of the Scottish Cup.
Johnny Russell's first-minute goal gave the Tangerines the perfect start and the striker also fired against the bar in the opening period.
Jon Daly's header doubled the hosts' advantage before the break.
Russell ended the tie as a contest with his second and Rangers had Kal Naismith and Ian Black sent off late on.
The build-up to the tie had been eventful, with Rangers deciding not to take up their ticket allocation when the teams were drawn together in December.
That step was a response to Dundee United opposing the Ibrox club's application to the Scottish Premier League months earlier.
Rangers had lost their SPL place due to financial problems and new owners tried unsuccessfully to enter the top flight before the Glasgow side were eventually placed in Division Three.
United chairman Stephen Thompson and Rangers manager Ally McCoist insisted on Friday it was time for the clubs to "move on", with the Taysiders eager to see how McNamara would fare a matter of days after replacing Peter Houston.
And the home fans were celebrating within 13 seconds as Emilson Cribari and Ross Perry allowed Daly's header to find Russell and he blasted the ball under the body of Neil Alexander.
The visitors, backed by 350 fans who had bought tickets directly from Dundee United, almost responded when Andy Little dragged a shot across the face of goal.
The hosts were doing their best to impress their new manager and a deep cross from Willo Flood was nodded just wide by the lively Russell.
Rangers looked vulnerable at the back every time a lofted ball was sent in the direction of Daly and another header from the captain set up Russell to flick the ball against the crossbar.
McCoist's side carved out a rare chance when Lee Wallace picked out Francisco Sandaza in the box, the former United striker glancing a header wide.
McNamara's new charges were soon two ahead, however, with Daly left unmarked to guide a deep Flood free-kick past the exposed Alexander.
Perry was replaced by Chris Hegarty after the loss of the second goal and McCoist's injury problems mounted with Naismith taking over from Sandaza at half-time.
Rangers improved after the break and Black's powerful drive swerved just past the post before David Templeton tested home keeper Radoslaw Cierzniak.
However, any prospect of a comeback was snuffed out when Russell got in behind Wallace to latch on to Daly's pass and flick the ball past Alexander 11 minutes from the end.
There was further misery for the visitors when Naismith was red-carded for a reckless lunge from behind on Flood, and Black soon followed his team-mate down the tunnel after his foul on John Rankin resulted in a second booking.
Dundee United will discover their quarter-final opponents when the draw is made on Sunday.