Graham Carey's first-half strike sent St Mirren through in their Scottish Cup fourth-round replay at Hamilton Accies and they now play host to Ross County.
Billy Reid's Accies almost snatched an early lead when Dougie Imrie nicked in ahead of Saints keeper Craig Samson and set up Jim McAlister, who shot wide.
But after 21 minutes Carey arrowed a low shot past Tomas Cerny from outside the box for the only goal of the game.
With three minutes left, Imrie struck the post with a 35-yard shot.
Saints named an unchanged side from the one that lost 5-2 to Hearts at the weekend, while Accies were boosted by the return of Mark McLaughlin from suspension.
After Imrie and McAlister had combined to give the Buddies that early scare, the visitors gradually began to impose themselves upon the match and David van Zanten was not too far away with a powerful shot from 20 yards.
St Mirren took the lead when Carey cracked a shot into the bottom corner but Accies could have hit back when Ali Crawford created space for himself only to squander a decent chance when he blasted well over.
McAlister then stung the palms of Samson with a blistering point-blank effort but the home side failed to find an equaliser before the break.
Accies emerged for the second half determined to haul themselves back into the tie and Dundee United target Imrie was unfortunate not to find the back of the net with a swerving effort that fell wide.
Carey curled a free-kick towards the top corner of the net but Cerny produced a great save to claw the effort away from goal.
With 20 minutes to go, Hamilton knew there was still time to rescue the tie and Imrie turned provider with a cross from the left for Lee Kilday but he saw his close-range header smothered on the line by Samson.
The home side continued to push for the leveller and Samson was called into action again to claim a bullet header from Accies top goalscorer McLaughlin.
Only the woodwork prevented Hamilton from drawing level with just three minutes to go when an audacious 35-yard strike from Imrie crashed off the post before the Saints defence frantically cleared the danger and held on for the win.
Hamilton: Cerny, Kilday, Canning, McLaughlin, Hendrie, Mensing, McAlister, Crawford, Andy Ryan (Martin 72), Anderson (Spence 71), Imrie. Subs Not Used: Hutton, Gordon, Devlin.
St Mirren: Samson, van Zanten, McAusland, Mair, Tesselaar, McLean, Barron, McGowan, Teale, Thompson, Carey (Thomson 86). Subs Not Used: Smith, Murray, Hasselbaink, Mooy.
Goals: Carey 21.
Referee: William Collum