Albion came back with two raids down the left flank. Robert Dunn swung in a centre which David McGurn stretched to latch on to before it found its way to the on-rushing Paul Di Giacomo.
McGurn then had to be at his best, diving away low to his left to divert a fierce Dunn drive round the post.
Morton stepped up the pressure to keep alive their promotion hopes.
McLaren's strike was deflected wide by a Paul Nugent challenge and a long-range shot from the experienced forward was well held by Myles Hogarth.
Millar's free-kick in the 16th minute was nodded on by the towering Chris Templeman for Ryan Harding to stab home from six yards.
Peter Weatherson fired over from 20 yards and Walker was extremely unlucky when, after clever hold-up play by Templeman, he swerved past two bemused defenders and cracked a powerful shot off the bar.
Di Giacomo forced McGurn into blocking a shot with his legs as Stirling began to move forward with more purpose.
Although Hogarth saved a Weatherson free-kick with a marvellous leap, The Ton were saved by McGurn who somehow tipped over a Nugent near-post flick from David O'Brien's corner.
Templeman finished off the visitors when he controlled a McLaren corner, jinked past his marker and slammed a low angled show past Hogarth.