Johnny Russell grabbed a double as Dundee United handed new boss Jackie McNamara the perfect start to the job with a 3-0 win to dump nine-man Rangers out of the cup.
Russell struck after just 16 seconds, before Jon Daly doubled the advantage and Russell put the gloss on the fifth round victory, which saw Kal Naismith and Ian Black dismissed late on.
Paul Heffernan's double sent Kilmarnock into the quarter-finals with a 2-0 win as Inverness suffered their second cup exit in eight days.
The substitute fired home in the 58th minute after Inverness were again exposed on the break, although they suffered an unfortunate run of the ball.
Heffernan's clever back-heel with five minutes left ensured Caley Thistle have now lost as many games in those eight days as they had in the rest of the season, with their Scottish Communities League Cup semi-final defeat by Hearts followed by a league defeat at St Mirren.
Esmael Goncalves continued his wonderful start at St Mirren with a brace in the 2-0 win against St Johnstone.
The 21-year-old took his goal tally to four in three games as the Buddies booked their place in the last eight.
Goncalves headed home to break the deadlock six minutes after half-time and doubled the hosts' advantage eight minutes later.
Hamilton ensured their progress with a 2-0 win over Irn-Bru First Division rivals Dunfermline at East End Park.
Steven May and Jonathon Routledge got the goals.
Falkirk eased into the quarter-finals with a convincing 4-1 win over Irn-Bru Second Division side Forfar.
Lyle Taylor (2), Stewart Murdoch and David Weatherston scored for Falkirk.
Iain Campbell was on target for Forfar.