This was one of those days when both teams took something from the game. Morton enjoyed their second big win in a week to further steady the ship after two defeats and move four points clear of promotion rivals Partick Thistle.
Bottom-of-the-table Alloa, despite losing for the fifth time in a row, showed far more shape and spirit than of late and have probably kept manager Tom Hendrie in a job.
The visitors were quickly in control and Jamie McAlistair slotted home the opener after 15 minutes when home keeper Gary McGlynn pushed Chris Millar's stinging drive into his path.
Full-back Steven Learmonth clipped the top of the cross bar for the Wasps but otherwise it was totally one-sided as McGlynn made excellent saves from Millar and McAlistair and Scott McLaughlin chipped fractionally over from fully 35 yards.
A crisp turn and firm finish from Derek Lilley doubled Morton's lead shortly before half- time, and only two more top class McGlynn saves denied Lilley his hat-trick in the second period.
Ross Hamilton struck the post for Alloa with barely five minutes left before substitute Jason Walker completed the scoring two minutes into injury time with a fierce shot high into the roof of the net from 12 yards.