The game was as good as over by half-time as two goals from Smith and another from Steven Doris saw the hosts leading 3-0 at the interval.
Smith completed his treble less than a minute into the second half with a brilliant 25-yard strike before Lewis McLear made it 5-0.
Sean Dickson and Doris again rounded off a miserable night for the visitors.
Darren Smith scored a hat-trick as Stirling brought Montrose's good recent run to a shuddering halt.