Celtic booked a place in the last four of the Scottish Cup with a 4-0 win over Dundee United in their quarter-final replay on Wednesday as both sides had a man sent off.

United arrived in Glasgow without a win at Celtic Park in nearly 23 years and never looked like changing that statistic or avenging last Sunday's League Cup final defeat after falling behind in the 17th minute to a header from Jason Denayer.

Leigh Griffiths volleyed home a second in the 57th minute before Kris Commons rounded off the scoring with a calm finish in the 79th minute.

The red mist descended in the final minutes as Celtic striker Anthony Stokes was sent off in the 87th minute for lashing out at Paul Paton following a challenge before Ryan McGowan was given a straight red for a hefty challenge on substitute Liam Henderson a minute later.

Virgil van Dijk tapped in a fourth in stoppage time as the Hoops progressed to April's semi-finals where they will face Inverness Caledonian Thistle.

"In the end it was a straight forward win, but there were some angry players out there so it got a little bit tense in the end," Celtic manager Ronny Deila said.

"I thought we played at a very high tempo for large parts of the game and it is very hard to cope with us."

Dundee United assistant manager Simon Donnelly had no complaints about the result.

"I don't think we can in terms of how we defended. They were bad goals to give away from our point of view," Donnelly said.

"We didn't do ourselves justice. Their second goal was a body blow and it was an uphill task after that."

In the third of four matches between the sides in 14 days, James Forrest was restored to Celtic's starting line-up in place of the suspended Stefan Johansen while Nadir Ciftci returned to lead the line for United after missing out of the League Cup final.

United had failed to finish with 11 players on the pitch in the previous two encounters between the sides and keeper Radoslaw Cierzniak forced referee Calum Murray in to a big decision with just under a minute gone when he clattered Griffiths outside the box, with the keeper relieved to only be shown a yellow card.

Cierzniak was then equal to an acrobatic effort from Griffiths before his goal was finally breached in the 17th minute. Denayer connected with a curling delivery into the box from a Stokes free-kick to send a looping header over the out-stretched hand of Cierzniak.

The home side had dominated possession but United almost pulled level just before the break when Craig Gordon got an all important touch on a cross from McGowan to prevent Ciftci from converting.

United started the second half with momentum, but it was the Hoops who added a second in the 57th minute through Griffiths.

The Scotland striker provided the finishing touch to a long ball over the top from Scott Brown as he sent a smart volley past Cierzniak in goal.

Moments after missing a good chance in front of goal, Commons added a third in the 79th minute. The forward picked out substitute John Guidetti and collected a return pass from the Swede before clipping the ball over the sprawling Cierzniak.

Stokes and McGowan saw red late on before van Dijk tapped in a pass from Denayer to finish the scoring in stoppage time.