With Shettleston chasing promotion the match was a vital one for both sides and the first quarter of the contest was really scrappy.
There were a series of free kicks and corners and from one of the flag kicks Shettleston's Rikki McIntosh headed past.
The same player then had another effort which also missed the target.
United, boosted by the return from injury of towering central defender Terry Hewitt, produced their best move of the opening period when Mikey McLaughlin set up Scott McHaffie whose shot was brilliantly tipped over by Shettleston keeper Gary White.
The visitors resumed after the break in determined fashion and a fierce effort from Ryan Scott smashed off the Cumbernauld crossbar.
In the 52nd minute ,however, Shettleston took the lead when a ball from the right wing was tucked away by striker Martin Welsh.
United responded immediately and when Jamie Watson was upended just outside the box, McLaughlin's free-kick just cleared the crossbar.
But in the 70th minute the home team got a deserved equaliser. A Murphy corner eluded the Shettleston defence and McHaffie, at the back post,slammed the ball past White.
Ten minutes later Cumbernauld had a great chance to take the lead.
Substitute John Higgins surged up the right and sent over a terrific ball to Watson. But the United front man's first attempt was blocked by White and his follow-up alsobrought out a great save from the visiting custodian.
Things looked ominous for Cumbernauld five minutes from time when, from a free-kick, confusion in the home defence gave Ross Dickson the opportunity to put Shettleston ahead.
But United had other ideas and threw everything at the visiting rearguard in the closing stages.
And they got their reward three minutes later when a great move involving Higgins and Davie Dickson set up Murphy to send an unsaveable 20-yard rocket past a helpless White to level.
But Andy Frame's side were not finished and when Hewitt was grounded in the box Murphy stepped up to take the resultant penalty, coolly beating White to give United a great victory.