St Johnstone reached the Scottish Cup semi-finals for the second year running thanks to a great first half display.
Rocco Quinn fired the First Division side ahead with a fabulous volley and Andy Jackson smashed in a powerful shot from the edge of the penalty area.
Peter MacDonald then curled in a sweet strike with just 28 minutes gone.
St Johnstone's Paul Sheerin had a penalty saved by Chris Smith before giving one away, from which Billy replied for the mis-firing Buddies.
The Perth side will meet the winners of Wednesday's Rangers v Partick Thistle tie in the last four of the tournament.
The home team carved out the first real chance of the game when Mark Corcoran's corner found the head of Ian Maxwell and his header dipped inches over the crossbar.
However, it was the visitors who quickly seized the initiative and they went ahead after 14 minutes when Liam Craig whipped in a cross from the left and Quinn connected superbly to send a volley past Smith.
MacDonald then pounced on a clearance from Saints goalkeeper Alan Main only to see his well-struck lofted shot nestle on the roof of the net.
However, St Johnstone did not have to wait too long for a second goal, which arrived with 21 minutes on the clock.
Paul Sheerin's long ball was dummied by MacDonald and collected 16 yards from goal by Jackson, who rifled past the helpless Smith.
St Mirren were then left with a mountain to climb when the visitors claimed their third of the night after just 28 minutes. This time it was MacDonald who left the net bulging with a lovely, curling effort from the edge of the penalty box.
The Perth side won a penalty early in the second half when Gary Mason was guilty of a foul on Jody Morris.
But Paul Sheerin, who has netted eight spot-kicks already this season, saw his effort pushed away by Smith at full-stretch.
There was further frustration for Sheerin when he conceded a penalty at the other end for handball.
Mehmet showed him how to finish from 12 yards by rifling low into the net with 20 minutes to go.
Boosted by the goal, Mason fired just over the crossbar from a free kick on the edge of the area.
Maxwell then saw his header skim over the bar but the belated rally from the SPL side failed to bear fruit.
St Mirren: Smith, van Zanten, Haining, Millen (McGinn 57), Maxwell, Barron (Kean 46), Mason, Dorman, Corcoran (Miranda 66), Dargo, Mehmet. Subs Not Used: Howard, Murray.
Booked: Dargo, Mehmet.
Goal: Mehmet 70 pen.
St Johnstone: Main, Irvine, Rutkiewicz, McManus, Sheerin, Quinn (Wilson 69), Craig, Morris, MacDonald (James 79), Milne, Jackson (Moon 54). Subs Not Used: Cuthbert, Weatherston.
Booked: MacDonald.
Goals: Quinn 13, Jackson 20, MacDonald 28.
Att: 4,596
Ref: D MacDonald
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