Aaron Mooy crashed in an early opener and Kyogo Furuhashi added a fantastic flicked finish before the interval.

Cameron Carter-Vickers scored a header late in the game to underline Celtic’s superiority at Tynecastle.

A wonderful save from Joe Hart denied Toby Sibbick at 1-0, with the home side seldom threatening thereafter.

Hearts were last season’s runners-up but hopes of reaching a fourth final in five seasons looked bleak following a whirlwind start from Celtic, who have a domestic clean sweep in their sights.

Inside the first minute, Zander Clark needed to look lively to push away a shot from Reo Hatate. Sixty seconds later, the Hearts goalkeeper was picking the ball out of his net.

Jota slalomed down the right before finding the Australian with a cutback, which was steered high into the net first time from 14 yards.

Hearts, who had scored early in Wednesday’s league meeting at Celtic Park only to fall 3-1, rarely got out their own half in the opening 25 minutes, struggling to match the pace and purpose of the visitors.

However, it took a marvellous save from Hart to preserve Celtic’s lead as the 35-year-old made an instinctive sprawling stop to claw away Sibbick’s close-range shot on the swivel. Hart was then up swiftly to prevent James Hill reaching the loose ball.

Clark was busy again, keeping out another effort from Hatate and knocking away a follow-up with his feet, but he was powerless to prevent Kyogo cleverly steering in a drilled cross from Alistair Johnston just before half-time.

Once again, the livewire Japanese striker lost his markers to net his 26th goal of the season with a deft clip.

Hearts made a determined start to the second half, although Clark added to his tally of saves with a good block from Jota’s angled strike.

Without top-scorer Lawrence Shankland and midfield veteran Robert Snodgrass through injury, the Edinburgh side were short on guile and Celtic did not need to work too hard to keep them at bay.

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Hatate thundered in a shot as Clark punched clear from a corner, with Hill making a crucial clearance, but the third goal arrived soon after as Carter-Vickers had the simple task of nodding in a curling free-kick from substitute Matt O’Riley.

Player of the match – Aaron Mooy

Fast and furious start sets tone for Celtic – analysis
Ange Postecoglou’s side stamped their authority on the match from the first whistle, completely suffocating Hearts with wave after wave of high-tempo attacks.

Celtic’s impressive midfield trio had an immediate grip on proceedings, controlling large parts of the game even as the pace dropped in the second half.

Both first-half goals came from Celtic’s right flank, with Stephen Kingsley exposed too often as Jota and Johnston galloped forward at every opportunity. Jota then switched wings to torment Michael Smith.

Hearts, missing a few key players, will look back at Hart’s incredible save to deny Sibbick but Robbie Neilson’s men never really recovered from the loss of such an early strike and were guilty of switching off at the back for the other goals.

They were also rather predictable in their pursuit of a way back, knocking hopeful long balls in the direction of Josh Ginnelly.

Celtic scored five in the previous rounds against Morton and St Mirren and could easily have had a few more today as they made it 13 successive wins in all competitions.

What next?
Runaway leaders Celtic host Hibernian on Premiership duty next Saturday (15:00 GMT), while Hearts visit Aberdeen at the same time.