David Hopkin's side fell behind after two minutes when a trialist gave the hosts the lead but levelled things up when a trialist of their own, wing-back Mark Davidson, headed home at a corner.
However, they were struggling to compete with their more experienced opponents and found themselves trailing 5-1 at half-time.
The Strollers scorers were David Anderson, Lee Davison, former St Mirren defender Peter Bradley, and the trialist centre forward, who added his second of the night.
Ton found their feet in the second half and restricted the hosts to one more goal from their trialist before the full-time whistle sounded on their Reserve League Cup campaign.
Head of youth Derek Anderson, who assisted Hopkin on the night, said: "The scoreline isn't great but it was good for the boys to be involved at reserve level. It's a real learning curve for them.
"We were disappointing first half; we needed to compete more from the first whistle. I thought the boys were a bit shell-shocked, to be honest. But there was a big improvement in the second half."
Morton (3-5-2): Murray [Trialist]; Jamieson (O'Hanlon), Mitchell, Tennent; Davidson [Trialist],O'Neil, Lamont (McEwan) (Langan), Cairnie, Knight; Ferris, Russell.