Celtic eased into the last 16 of the William Hill Scottish Cup with a comfortable 4-0 win over 10-man Hearts at Tynecastle.

A difficult task for the Championship leaders became daunting in the eighth minute when home skipper Morgaro Gomis was shown a straight red card by referee Willie Collum for his challenge on Hoops counterpart Scott Brown.

Celtic took advantage of the extra man, although they had to wait until the 28th minute before defender Virgil van Dijk shot them into the lead following a corner.

However, the second half quickly turned into a rout.

John Guidetti scored his 11th of the season with a penalty in the 51st minute and fellow forward Anthony Stokes made it 3-0 with a drive three minutes later before Van Dijk headed in a Stefan Johansen corner for his second of the game as the Parkhead men showed no mercy.

Gomis dismissal was undoubtedly a pivotal moment, but at the end of a dispiriting afternoon Hearts were probably glad that the 7-0 scoreline from the same stage of the competition last season was not repeated.

If Hoops manager Ronny Deila is to win the treble he so badly covets this season, then Guidetti will surely be key.

The Swede, ineligible for the Hoops' 3-1 Europa League home defeat to Salzburg on Thursday night, returned to lead the attack with winger, James Forrest and Nir Bitton also coming in.

The Championship leaders showed two changes, with former Celtic man James Keatings and Adam Eckersley in for Kevin McHattie and Soufian El Hassnaoui.

The travelling fans took up their full 3,500 allocation for the Roseburn Stand, but surprisingly Tynecastle was not full for a traditionally explosive fixture which again did not fail to disappoint.

In the second minute Celtic goalkeeper Craig Gordon, back at Tynecastle for the first time since he left Hearts to join Sunderland in 2007, was forced into a decent save from Keatings' drive from the edge of the box.

However, the dynamic soon changed.

Gomis was unhappy at the manner in which Celtic midfielder Johansen tried to rob him of the ball and seconds later he went looking to get it back off Brown in the centre circle.

The former Dundee United midfielder's challenge was two-footed and lacked control, but when Collum brandished a red card the Hearts supporters exploded in anger.

It was a volatile few minutes which followed as the enraged home fans looked for Collum to even up the numbers every time a Hoops player put in a tackle.

The visitors, understandably, took control of the game and began to wear down the Hearts rearguard and eventually they got the breakthrough.

Johansen's corner from the right made its way to the far side of the box and, when Stokes turned the ball back into the pack with what looked like a wayward shot, Van Dijk calmly steered it past Gorgie keeper Neil Alexander from 16 yards.

The Dutchman should have made it 2-0 in the 37th minute when he met Stokes' corner from the left, but somehow he lifted the ball over the bar from a couple of yards out.

It was difficult to see a way back into the tie for the Tynecastle side.

When defender Brad McKay was adjudged to have tripped Guidetti in the box five minutes after the restart, allowing the Manchester City loanee to sweep the penalty into the corner of the net, only the margin of victory was up for debate.

Stokes added a third three minutes later with a low drive from the edge of the box before Van Dijk rose to head Johansen's corner past the helpless Alexander.

Hearts looked demoralised.

Kris Commons and Leigh Griffiths came on for Stokes and Johansen respectively as Celtic looked to pile on more goals.

The former had the ball in the net in the 78th minute after Alexander saved a drive from another Hoops substitute, Aleksandar Tonev, on for Forrest, but referee Collum blew for an infringement on the keeper.

Hearts substitute Robbie Buchanan, on for Jamie Walker, fired inches wide in a Gorgie breakaway, but it was a mere footnote as the match petered out to the sound of celebrating Celtic supporters.