The New Saints stayed on course to be only the second Welsh team to reach the SPFL Trust Trophy final with a 4-1 hammering of Arbroath.
They will be joined in the semi-final draw by Airdrieonians, Falkirk and Raith Rovers.
Falkirk caused the shock of the round with a 4-2 defeat of favourites Dundee United on Friday as Rovers won 4-1 away to Hamilton Academical.
Airdrie edged hosts Greenock Morton 6-5 on penalties after a 0-0 draw.
Jay Bird opened the scoring for Scottish Championship side Arbroath after only nine minutes in Oswestry.
However, the Welsh champions hit back through Ben Clark and Brad Young to lead 2-1 at half-time.
Two goals in the last 10 minutes from Adrian Cieslewicz and Young secured a last-four place.
On Friday, Callumn Morrison put League 1 leaders Falkirk ahead against their Championship counterparts after only four minutes.
Mathew Anim Cudjoe and Tony Watt had United ahead by the break, but three goals in six second-half minutes from Tom Lang, Finn Yeats and Morrison put the home side through.
Raith were ahead against Hamilton through an early Sam Stanton goal, and Accies' hopes of a comeback suffered a blow when Lee Kilday was sent off nine minutes after the break.
Jack Hamilton scored twice to extend the lead and, although Dario Zanatta replied for the League 1 side, Dylan Easton restored the three-goal margin.