St Johnstone shook off the dejection of their mauling by Aberdeen in last week's League Cup semi-final to reach the Scottish Cup last eight.
Forfar keeper Rab Douglas, making his 499th senior appearance, was beaten four times as the League One side succumbed to their top-tier opponents.
Stevie May scored his 21st goal of the season with a clever hooked shot and Frazer Wright headed home the second.
After the break Michael O'Halloran and James Dunne made the result certain.
Saints midfielders Croft and McDonald were key figures for the visitors to Station Park, with the latter very unfortunate to have had a headed goal ruled out for an infringement.
But it was from Croft's corner kicks that Tommy Wright's team scored their first two goals and from his efforts on the right that goals three and four arrived after the interval.
In 27 minutes McDonald rose to meet the Englishman's lofted delivery and the ball fell, somewhat fortuitously to May, who spun and hooked a shot beyond the 41-year-old goalie for the opener.
Forfar left-back Iain Campbell had positioned himself on the goal-line but he too was unable to clear.
It was a sore one for Forfar for whom Martyn Fotheringham had hit the post five minutes earlier with a left-foot shot.
Saints's second goal had a similar feel. May and Wright ran towards the front post at Croft's corner but McDonald stayed put and headed powerfully at goal where Douglas could parry only as far as Wright who headed home from three yards.
After the break David Wotherspoon was allowed time and space to weave towards the Forfar box and his left-foot strike whizzed narrowly over the crossbar.
Forfar, to their credit, did enjoy some decent passages of play.
St Johnstone's Stevie Banks parried a powerful Ross Campbell shot over the bar and Odmar Faeroe hammered a shot a few feet wide of the keeper's right-hand post, having hit the crossbar earlier.
O'Halloran underlined the Perth team's superiority as he thumped home the third goal of the game.
Douglas could only divert Croft's angled shot into the new signing's path and he finished confidently from eight yards.
May went close with an ambitious curler that floated a fraction wide of Douglas's left-hand post before sub Dunne rounded off the scoring.
Again, Douglas could only parry a ball in by the industrious Croft and Dunne was well placed to finish with a volley.
Forfar really ought to have got on the scoresheet right at the end when Campbell's low cross from the right was met by Gavin Malin but he knocked his sliding effort wide.
Forfar manager Dick Campbell:
"I'm disappointed. Our record in the Cup is better than that.
"I didn't realise St Johnstone were as good a side as that so all credit to them and their manager.
"Their first goal was a set piece. The boy May has taken it well. I can see how he is an exciting prospect.
"I thought at 1-0 we had a game but they scored right on half time and that made it a real tall order for us.
"We had a better response in the second half.
"We had three or four chances but their finishing was clinical and their possession was good as well, which we'd expect from a full-time side.
"We kept on trying and having a go but you could see the difference between the Premier League and the Second Division today.
"Rab Douglas hadn't a save to make in 38 minutes apart from picking the ball out the net twice. It's not as if they were peppering the goal with shots or whatever."
St Johnstone manager Tommy Wright:
"It's important to come here and have the right attitude. We had that, particularly in the first half.
"To win away from home is very pleasing and it's important because we are in the next round.
"We had worked on a few things in corners this week in preparation for this game. We got it at the back post and Stevie picked up the second ball and then Frazer scored off a corner as well.
"Stevie has had a great season and hopefully he can continue to score goals.
"I must give Forfar a bit of credit. In the first 10 minutes of the second half they put us under pressure.
"Banksy made a good save and we made a few blocks but then we took more control of the game and I'm pleased for Michael. He's been trying to get a first-team place and he took it well today and James has just come in and he had a great finish.
"Lee's fully fit now. He didn't play a lot of football, not having a club, and it has taken him a couple of months to get him to the level that we want.
"I think we'll see a lot of Lee from now until the end of the season and the benefits of what a good player he is."
- 01 Douglas
- 02 Baxter
- 03 Campbell
- 08 Fotheringham (Hilson - 46' Booked )
- 04 Malcolm
- 05 Dods
- 07 Kader (Campbell - 69' )
- 11 Fusco
- 10 Swankie
- 09 Templeman
- 06 Faeroe (Malin - 72' )
- 12 Campbell
- 14 Andrews
- 15 McCabe
- 16 Malin
- 17 Dale
- 18 Hilson
- 20 Hill
- 15 Banks
- 02 Mackay
- 24 Easton
- 04 Cregg
- 05 Wright
- 06 Anderson
- 22 Croft
- 08 McDonald (Brown - 82' )
- 29 O'Halloran Booked
- 17 May (Iwelumo - 77' )
- 10 Wotherspoon (Dunne - 69' )
- 07 Millar
- 11 Hasselbaink
- 12 Dunne
- 19 Miller
- 20 Brown
- 25 Iwelumo
- 35 Hurst
Ref: John Beaton