Montrose were on top from the start and they opened the scoring after 11 minutes. Barry Donnachie played a ball through and Greig Henslee supplied a fine finish.
Montrose piled on the pressure, and after 23 minutes a long kick from Andy Reid released Henslee, but keeper Derek Jackson saved with his feet.
A minute later Steven Kerrigan set up Euan Hall and his shot was turned round the post by Jackson. Just seconds later Hall set up Kerrigan and again Jackson did well to save.
After 32 minutes a fine drive from Kerr Dodds was tipped over by Jackson.
Montrose stretched their lead after 35 minutes when Kerrigan turned superbly and crossed for Henslee to head home.
A minute from half-time Martyn Fotheringham missed a sitter from a Kevin Webster cross.
East Stirling began the second half well, and Iain Diack forced a fine save from Reid.
Martyn Fotheringham incredibly missed another gilt-edged chance after 63 minutes from a Henslee pass.
Montrose made it 3-0 after 67 minutes when Henslee chested home a corner to complete his hat-trick, despite the efforts of two defenders to clear the ball off the line.
Montrose continued to press and Fotheringham shot over from 25 yards, and then Fotheringham sent an over-head kick wide from a Webster cross.
Eight minutes from time, Kerrigan headed the ball on and substitute Willy Martin lobbed the ball into the hands of Jackson.