Kabba-Modou Cham fired David Hopkin’s side into a sixth-minute lead with a glancing header from an excellent Cameron O’Neil cross.
But ex-Ton man Ryan McGuffie drew the visitors level 20 minutes later when he headed home a free-kick via the post.
Queens then took the lead through a stunning strike shortly before half-time and looked to have the points in the bag until the Cappielow club’s late show.
On 84 minutes, David McNeil rifled in an equaliser from close range after trialist striker Dylan Connor’s original effort was blocked.
And 17-year-old frontman Aidan Ferris completed the turnaround when he netted an almost identical strike three minutes from time, taking his tally to six goals in three starts and two sub appearances.
Morton (4-1-3-2): Caraux (6); Knight (7), Cairnie (6), O’Ware (7), Russell (7); Verlaque (5); O’Neil (7), Stirling (5) (Connor 46, 5), Fulton (6) (Lamont 79, 4); Cham (6) (Ferris 69, 5), McNeil (6).
Sub not used: Eadie.