A draw and penalties reverse at Stranraer on Saturday had left Motherwell five points off the top of Group G, but Sammon netted twice in the first half as Motherwell triumphed 2-0 at Fir Park.
Stephen Robinson’s side will now definitely progress if they win at Clyde on Saturday.
Queens were the first team in the competition to reach nine points and arrived at Fir Park as the top scorers with 12 so far.
The Championship side had the better of an action-packed opening spell as Stephen Dobbie was twice denied by Trevor Carson, who also saved well from Callum Semple.
Motherwell threatened through Richard Tait and Carl McHugh before taking the lead in the 12th minute, when Chris Cadden burst from the halfway line before slipping the ball through for Sammon to net his first goal since joining on loan from Hearts.
The goal settled Motherwell and Sammon doubled the lead in the 37th minute when he ran on to Ryan Bowman’s header-on, skipped past a defender and slotted the ball just inside the post.
Queens became more threatening after Motherwell lost Bowman to injury after a poor challenge by Semple, but Carson pulled off a fine one-handed save from a Gary Harkins header. That save seemed to suck the belief out of the visitors and Sammon was denied a hat-trick by Alan Martin.