St Johnstone set up a trip to Glasgow to face the winner of Sunday's Old Firm shoot-out as they eased past Clyde 2-0 at McDiarmid.
There looked to be a mismatch on the cards as Guy Melamed and Michael O'Halloran put Callum Davidson's team two up after just 21 minutes.
But the Perth men could afford to take their foot off the gas and still cruise into the last eight of the Scottish Cup.
And they will now watch with eager interest as Rangers and Celtic clash at Ibrox for the right to host this season's Betfred Cup winners in the next round.
Davidson chose to give Hampden heroes Zander Clarke, Callum Booth, Shaun Rooney, Ali McCann and Chris Kane a rest ahead of Gers' Scottish Premiership visit on Wednesday night.
This was Clyde's 10th game in the space of 22 days and with a vital League One relegation crunch against Forfar to come on Tuesday, Danny Lennon also chose to leave out a string of regulars, including former Scotland striker David Goodwillie.
It was evident early on that Clyde's hectic schedule had left little in the tank as they stepped up to face top-flight opposition.
If the part-timers were to stand any chance, they needed to avoid conceding an early goal.
But those hopes went up in smoke inside six minutes as Melamed caught Lloyd Robertson in possession.
O'Halloran drove into the box, delaying his cross by a fraction of a second to ensure the Israeli could steer home from five yards out on the stretch.
The Bully Wee were making problems for themselves trying to play out from the back.
But it was a lucky break that handed St Johnstone their second as a wild bounce from Scott Tanser's block tackle on Marky Munro sent Stevie May surging down the left, with his ball inside perfectly measured for the onrushing O'Halloran to stick through Matej Vajs' legs.
Jamie McCart was denied a first goal for Saints just before the break as Munro cleared from under his own crossbar.
The big centre-back blazed another over in the 65th minute as Saints continued to rack up chances.
Skipper Liam Craig had a couple of efforts pushed away by Vajs while Melamed thudded a David Wotherspoon corner against the crossbar with his head.
Lewis Jamieson thought he had given Clyde a lifeline with 12 minutes left after Liam Gordon miscontrolled a hospital pass from goalkeeper Elliott Parish – but the Saints defender's blushes were spared by an offside flag as the top-flight outfit claimed their fourth clean sheet in their last five games.
