Ben Tilbury scored twice, including a fourth minute opener, as the hosts took advantage of some lax defending to win the first round tie.
Shifnal found themselves two down at the break when Ben Jevons diverted home Lee Chilton’s corner and then had a mountain to climb when Tilbury smashed home again within three minutes of the restart.
The visitors finally began to exert some pressure and pulled one back when Max Chimenes drove a shot beyond Stourport goalkeeper Josh Bishop.
Yet any hope of a comeback was quickly extinguished when Chilton hit home to restore the home team’s three-goal cushion.
Shifnal, to their credit, kept pushing. Joe Thompson came close to pulling a goal back just past the hour mark and then did reduce the deficit from the penalty spot after Jevons had bundled over Chimenes. But it proved only a consolation.
Jayden Hunter marked his debut for Whitchurch Alport with the goal which set them on course for a 3-0 win over Uttoxeter in the Midland League Premier Division.
Hunter, who joined last week on loan from Newcastle Town, fired home just before the half-hour mark. Second half goals from Sam Yeardley and Nicky Parker completed a victory which saw Alport move up to ninth in the table.
“It’s up there certainly with some of our best performances. Definitely in the top three,” said assistant boss Adam Shillcock.
“It was a 16-man game today. The subs who came on all had an impact. I am pleased for everyone.
“Jayden could have had four or five goals. We have brought him in because we know what he is about.
“He has a yard of pace and can get into goalscoring positions. It was certainly an encouraging first game for the club but there is a chance now to kick on and go and score goals for us. But he has had a really good start.
“Our standards at the end of the game to try and keep a clean sheet were absolutely bang on. I thought the performance in general was perfect.”