The Premiership side ran out 3-0 winners but had difficult moments and the home team were denied a stonewall penalty in the first-half when Dundee led 1-0.
Progression for James McPake’s side means it is an all-Premiership affair in the quarter-final with Celtic and Rangers travelling to face Dundee United and Dundee respectively. Motherwell will host Hibs and Hearts welcome St Mirren to Tynecastle Park. The eight teams know they are just one win away from returning to Hampden Park.
Ties are scheduled to take place on the weekend of March 12 with the likelihood none will be played at 3pm on the Saturday due to TV coverage as Premier Sports and BBC have access to two ties each.
Meanwhile, there is a big game in the Premiership this evening as Aberdeen host St Johnstone. The Dons can jump back into the top six with a win, while the Perth Saints will be looking to get off the bottom of the league.
Barry Robson is in interim charge at Pittodrie, aided by Scott Brown and Neil Simpson, while the hierarchy search for a new manager.
Robson said: “I am employed by Aberdeen and I want them to do well. It is never easy when a manager loses his job. I have experienced it many times as a player and as a coach."
Scroll down and click through for all the latest news and speculation from around the SPFL and Scottish football.
5. Solskjaer tipped for Dons job
Former Aberdeen star Charlie Nicholas reckons the Dons should make an ambitious play for Ole Gunnar Solskjaer. The Norwegian is out of work after his spell at Manchester United. Nicholas said: “ Solskjaer's CV outwith Old Trafford is Molde and Cardiff City - two clubs of similar size and potential to Aberdeen. Why shouldn't Dave Cormack show some ambition and try to get a big name to reignite the fire at Pittodrie?" (Daily Express) Photo: IAN KINGTON
6. Ferguson's Rangers dream
Barry Ferguson has admitted he would love to go back to former club Rangers. He took the decision to step away from Alloa Athletic, admitting it wasn’t working and needed something different. On a possible Ibrox return, he said: "I don't care what level it is, whether it's 11-year-olds or a seasoned pro, at some stage I would love to get back to Rangers.” (Go Radio) Photo: Ross MacDonald - SNS Group
7. Scottish transfer markets
Ange Postecoglou reckons Scottish clubs are focused on certain markets when there are others out there to explore. The Celtic boss pinpointed Hearts as an example with their use of the Australian market with the signings of Cammy Devlin and Nathaniel Atkinson. He said: “I look everywhere, mate. I don't look at one market. Here, they seem to be focused on certain markets but I know talent can be found anywhere in the world, including Australia.” (The Scotsman) Photo: Craig Foy - SNS Group
8. Rangers not forced to sell without CL football
Rangers managing director Stewart Robertson has revealed the club won’t be forced to sell players if they don’t reach the Champions League group stages. The league winners are all but assured qualification for the lucrative stage. He said: “The long-term viability of the club is first and foremost and that means trading players. It doesn’t mean just selling players. We don’t budget to be in the Champions League.” (Sky Sports) Photo: Ross MacDonald - SNS Group