Motherwell - who fielded Christian Ilic and Ross Maciver in place of crocked Chris Long and Jermaine Hylton - made it three clean sheets in a week when they drew 0-0 against Hibernian at a chilly Fir Park on Saturday.
This completed a hugely satisfying seven days for the Steelmen which also featured a 3-0 William Hill Scottish Cup fourth round romp at Dundee and a battling 1-0 league success over Aberdeen at Pittodrie.
The first chance for Motherwell against Hibs arrived on four minutes when James Scott beat a defender on the left flank, cut inside and rasped a 20-yarder not too far wide.
A swift 12th minute Hibs attack then saw Martin Boyle sprint at the home defence and pass to Florian Kamberi whose dangerous cross from the right flank was well headed clear by Peter Hartley.
Motherwell had an excellent chance with a free-kick from the edge of the box on 22 minutes but Jake Carroll's powerful drive was too straight at away keeper Ofir Marciano. The dangerous Scott then did well again on the left and his cross was missed by Maciver in the middle.
A free-kick into the Hibs box then fell for the outstanding Allan Campbell who volleyed wide with his right foot.
Motherwell's Liam Polworth then sent an ambitious 25-yard drive just over the Hibs bar on 29 minutes.
Liam Donnelly was next to have a crack at goal from distance for the hosts but the ball again sailed over the bar.
Motherwell survived a scare on 52 minutes when Gallagher gave the ball away to Horgan who advanced and struck a shot which was parried out by Gillespie. When the ball was played back into the area, Kamberi headed against the inside of the far post.
A spell of 'Well pressure then saw Scott send in a shot saved by Marciano after a Maciver pass, before Donnelly's 25-yard drive was deflected past.
A 68th minute Hibs breakaway ended with Horgan shooting off target. Horgan then sent a headed chance weakly at Gillespie.
Motherwell came agonisingly close to breaking the deadlock on 79 minutes when tenacious play by Campbell sent substitute Christy Manzinga through and his goalbound effort was brilliantly touched onto the bar by Marciano.
Roared on by the home crowd, the Steelmen kept pressing until the end but couldn't muster a winning goal.
Motherwell: Gillespie, Carroll, Grimshaw, Hartley, Campbell, Ilic (Seedorf 61), Scott, Polworth, Donnelly, Gallagher, Maciver (Manzinga 74).
Referee: Colin Steven