Sander Kartum lit up Tynecastle with two superb goals as Hearts booked their place in the Scottish Cup semi-finals at the expense of Dundee.
The January signing from Brann broke his Hearts duck with a stunning strike from 20 yards to give the hosts a first-half advantage.
Joe Shaughnessy nodded in Ziyad Larkeche's cross for parity after the interval but Simon Murray's headed own goal from Blair Spittal's free-kick put the hosts ahead again.
And Kartum spun and sliced a low shot through the Dundee defence to ensure Neil Critchley's side progressed to the last four.
"We've seen the quality Sander has," head coach Critchley told BBC Scotland.
"He's been getting better and better in training. On his left foot around the edge of the box, that's what he can do. They were two fantastic, match-winning goals."
Elton Kabangu, Calem Nieuwenhof and Alan Forrest were denied by Trevor Carson as Hearts pressed for a more emphatic victory.
The semi-final draw takes place live on BBC Scotland and iPlayer following Livingston v St Johnstone on Monday night. Aberdeen host Queen's Park on Saturday and Hibernian visit holders Celtic on Sunday.
Critchley and his players can spend the next three days sizing up their potential opponents on the weekend of 19 and 20 April.
They begin their Hampden build-up on 15 March at home to Scottish Premiership opponents Ross County.
Premiership survival now becomes Dundee's focus, with a derby at United next up for Tony Docherty's men on 16 March.