The young winger gained huge confidence after etching his name on the scoresheet for the first time since cartilage damage in April.
Hearts dominated large portions of the match against a strong St Mirren team containing club captain Stephen McGinn and midfielder Oan Djorkaeff.
Anthony McDonald opened the scoring on 37 minutes, planting a left-footed finish into the bottom corner after Aidan Keena’s clever through pass.
Saints struck the frame of the Hearts goal twice early in the second half before Morrison converted at the back post following Keena’s run and cross.
This Group C tie was put to bed just after the hour mark in bizarre circumstances. The hosts’ goalkeeper Kelby Mason launched a goal kick upfield and St Mirren’s Scott Glover attempted a back header, but the ball arced over his keeper Dean Lyness.
The visitors reduced the deficit 19 minutes from time with a penalty. Cameron MacPherson converted after the Hearts defender Cammy Logan was judged to have handled in a sliding block tackle near his own goal line.
Hearts (4-2-3-1): Mason; Logan, Hamilton, Petkov, Baur; Cochrane, Bozanic; Morrison (C Smith 65), McDonald, Henderson; Keena. Unused subs: Silva, Sandison, Ritchie, McGill, Ward, Darge.
St Mirren (4-3-3): Lyness; McAllister, Baird, Glover, Erhahon; McBrearty, McGinn, MacPherson; Djorkaeff, Jack, Breadner.