Craig Wight was called into early action for the Lions as Paul Lovering's cross was met by Brian McPhee at the back post. The keeper pulled off an acrobatic save to tip the ball wide just as it seemed certain to nestle in the top corner.
It took until the 26th minute for the home side to take the lead in the match.
A quick free-kick by Lee Makel that caught the away defence slumbering allowed former Motherwell striker Steven Craig a clear path to goal.
The hitman rifled his drive into the bottom corner leaving Stephen Robertson with no chance of making the save.
Just before half time and the home side struck again. A near post corner from Joe Hamill was flicked to the back post for centre-half James McPake to race in and score with the simplest of headers.
Graeme Holmes thought he had equalised for the Diamonds only to see his shot blocked on the line by full-back Dave MacKay midway through the second half.
Livingston put the game out of reach of the visitors in the 65th minute when Scott Mitchell's shot ricocheted straight back into the midfielder's path, allowing for a second bite of the cherry which ended up in the bottom corner of the net from just outside the box.