Holders Hibernian beat Edinburgh rivals Hearts to set up a home Scottish Cup quarter-final with Ayr on 4 March.
Jason Cummings latched on to substitute Andrew Shinnie's clever pass to give Hibs an early lead.
Cummings turned provider for Grant Holt's strike as Hearts fell two down before the break.
And Shinnie, who had replaced Chris Humphrey early on, rifled in the hosts' third in the second half, Esmael Goncalves replying for Hearts.
Hearts found themselves engulfed at the home of their closest rivals. The visitors had expected Hibs to start the game assertively, but the intensity and commitment still saw their resolve collapse.
Hibs were canny in their approach, since the vivid pace of Martin Boyle and Humphrey on the flanks was enough to alarm the Hearts full-backs. The latter only lasted four minutes, due to injury, but a series of crosses from the right by both wingers led to desperate Hearts defending.
The opening goal was typical, with Hibs swarming upfield and Shinnie having the presence of mind to split the Hearts defence with a through ball that allowed Cummings to finish with a powerful and precise finish - continuing his scoring record against Hearts after netting the winner in last season's fifth-round replay.
The second goal was agonising for Ian Cathro's side, since they conceded possession deep in their opponents' half through a sloppy Lennard Sowah pass, then found themselves further behind after three passes and a counter attack ended with Holt slipping home.Holt's previous goal had come in late October
Hibs' tenacity was irrepressible. John McGinn set the tone in the second half when he carried the ball into the Hearts penalty area, lost it, but then won it back with such eagerness that the visiting defenders looked forlorn. He cut a pass back to Shinnie, and his effort was saved one-handed by Jack Hamilton.
Every Hibs figure was fully in command. When the home fans grumbled angrily at a misplaced pass, head coach Neil Lennon turned to the stand and beckoned them to calm down. When they applauded in response, he lifted his arms to raise the atmosphere.
McGinn, too, was a forceful presence in midfield. It was his determination to win the ball that led to Shinnie striking an effort from 20 yards that seemed to fly through Hamilton's hands for the decisive third goal.
By the end, the home fans were chanting "there's only one Ian Cathro" in mocking tones.
Walker stands alone
The Hearts head coach did not need a squad so much as the ability to clone Jamie Walker. The attacking midfielder was the sole figure of defiance in his side, but had to roam the field looking for a way to influence the game that he was mostly isolated.
Alexandros Tziolis is a clever, accomplished footballer, but he seemed at odds with the pace of the game. Malaury Martin looked like a player who had found himself in the wrong game.
He did not re-emerge for the second half, along with Perry Kitchen, but with Hibs so well organised and drilled, even the addition of a winger in Sam Nicholson and a forward in Rory Currie could not disrupt them.
Nicholson did create a chance for Walker, which he sent over, and Currie did win the ball before sending it to Goncalves, who was fouled by Darren McGregor for a penalty.
Goncalves took the spot-kick, but even that was half-hearted and Ofir Marciano saved twice before the striker eventually bundled the ball over the line.
It was too little, too late, and on the final whistle Walker sank to the ground, alone in feeling too deflated to stand. He was also the only one of the Hearts players to head towards the away fans to applaud them before he left the field.Goncalves netted his first Edinburgh derby goal