Albion and Morton will meet again in the William Hill Scottish Cup after Peter Weatherson's second-half goal forced a replay following a 1-1 draw.
The visitors are unbeaten since August and they made a bright start against their Second Division opponents as David O'Brien forced goalkeeper Matthew McGinley into an early save with his feet.
Archibald Campbell then fired wide while at the other end, Anthony Stevenson's curling effort was held by Morton stopper Derek Gaston.
McGinley again made use of his feet to repel Weatherson and Albion were able to head into the break in front as Stevenson struck in first-half stoppage time.
The defender kept his composure as he slammed home a rebound on the volley from 12 yards out.
But Morton fought back and Weatherson applied the finishing touch to Michael Tidser's teasing free-kick to restore parity after 58 minutes.