Oran Kearney's team triumphed 2-0 on penalties after a tense match finished 1-1 after extra time, following a 0-0 draw at Tannadice on Thursday. Nicky Clark gave the visitors the lead from the spot midway through the first half but Danny Mullen quickly equalised for the Buddies.
Saints had substitute Duckens Nazon sent off towards the end of extra time but they held their nerve in the shoot-out while United missed all four kicks.
Penalty shoot-out summary
0-0 Peter Pawlett missed
1-0 Paul McGinn scored
1-0 Pavol Safranko missed
2-0 Mihai Popescu scored
2-0 Osman Sow missed
2-0 Mateo Muzek missed
2-0 Callum Booth missed
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