Beating their Midland Premier rivals at Yockings Park, Luke Goddard’s charges were two to the good after just 20 minutes in the first qualifying round tie.
Temi Ajibola opened the scoring as he fired past Adam Harrison, with Joe Minshall heading home soon afterwards.
A sweet strike from Jud Ellis at the death made sure of Alport’s place in the next round, and Alport director of football Lea Edge said: “For the whole 90 minutes, we played well.
“We had a good shape. We stuck to the plan. We took our chances in the first half and over the 90 minutes, we could have won by five or six.
“Defensively, I thought we were superb and the midfield shape was a lot better.
“So, overall, it was a really positive performance.
“The lads dug in as a squad. We’ve got a lot of injuries, so we’re pretty threadbare, but they kept going.
“They kept that shape we demanded. When bodies needed to be chucked on the line, we did it.”
Alport are set to host Pershore Town next in the competition on Saturday, September 25.
Shifnal Town also made it through with a comfortable 5-1 win against Khalsa Football Federation, with Tom Hill grabbing a hat-trick.
Danny Carter’s side took the lead as Jordan Uppal played a fine ball down the left for Jake Webb, who turned inside and fired into the bottom corner.
Town doubled their advantage as Hill slid home from 12 yards, and he soon got another to make it three going into the interval.
Hill completed his treble on the hour, heading home a cross from Keefe Williams.
Webb made it five before Adam Nazir’s late consolation for the visitors.
Shifnal will travel to Boldmere St Michaels in the next round.
AFC Bridgnorth were the other Shropshire side to make it through, beating Rocester 2-1 at Crown Meadow.
Haughmond were knocked out by Ashby Ivanhoe, losing 3-2, while Shawbury United were downed 4-0 by Romulus.
St Martins endured a record-breaking 18-0 thrashing at the hands of Hinckley.
Former Haughmond assistant Josh Gough has been appointed as their new boss in the wake of the heaviest loss in the history of the competition. It is also the club’s biggest-ever defeat.
Finally at the weekend, in the North West Counties First Division South, Ellesmere Rangers drew 1-1 with Wythenshawe Amateurs. Joe Parry scored for Ellesmere.
Tonight in Midland One, Shawbury host Bridgnorth at the Ludlow Stadium.
In the Premier Division, Haughmond welcome Shifnal to Shrewsbury Sports Village and Alport go to Wolverhampton Casuals.
On Alport’s trip to Casuals, Edge added: “We’ve shown that we can score goals this season.
“The frustration has been the goals we’ve conceded.
“We’ve got two wins on the bounce now and if we can get something, we’ve got two home games where we can build.”