Celtic break Hearts again to reach Scottish Cup semi-final
Hearts are on track to finish third in the Premiership behind Celtic and Rangers for the second consecutive season.
But the gulf between the Old Firm and the rest only appears to be growing as they were beaten by Ange Postecoglou's men for a second time in four days.
Celtic have already retained the League Cup and are nine points clear of Rangers in the league title fight.
An early strike from Aaron Mooy put the Scottish champions on course for the last four.
Kyogo Furuhashi then took his tally for the season to 26 with a delightful backheel finish from Alistair Johnston's cross just before half-time.
The visitors eased off after the break, but still grabbed a third 10 minutes from time when Cameron Carter-Vickers headed in Matt O'Riley's free kick.
"We started really strong and knew we had to. When you come to Tynecastle, you don't want their crowd to get up too much," said Postecoglou.
"We got our goal and overall controlled the game well."
Rangers are the only other top-flight team left in the competition ahead of their quarter-final clash against Raith Rovers on Sunday.
Second-tier Inverness are through to the last four after beating Kilmarnock 2-1 on Friday.
League One Falkirk take on Ayr United of the Championship in the other quarter-final on Monday.