The victory, their sixth on the trot, sees David Hopkin's side leapfrog erstwhile leaders Airdrie United to reclaim top spot in the SFL reserve league table.
After finding the net with a superb strike in the reserves' recent 3-1 win over Rangers at Murray Park, Aidan Fulton was rewarded with a place in the starting line-up.
And the 18-year-old left-winger grabbed the opportunity with both hands by playing an instrumental part in his side's first and second goals.
In the 31st minute, he whipped over an outswinging corner from the Cowshed side which Thomas O'Ware met with a bullet header to open the scoring.
Six minutes later Fulton repeated the trick from the opposite side, picking out Lewis Hawke who, in turn, looped a controlled header back over Annan goalkeeper Daniel Tobin and into the top-right corner.
Kyle Wilkie added a third just after the hour mark, slamming home from inside the box after Daniel Moss's fancy footwork and flick created the opening.
And left-back Jordan Halsman wrapped up the scoring 15 minutes from time when his cross floated over Tobin and dropped into the net off the post.
Morton (4-4-1-1): Hutton; Taggart, Naismith, O'Ware, Halsman; Frizzell, Wallace, Wilkie (McLean, 67), Fulton (McDaid, 63); Moss; Hawke (D. McLaughlin, 73). Subs not used: Keogh, Jamieson.