The third-tier visitors had threatened an upset when, having had just 15 per cent possession, they took a 27th-minute lead through Daniel Udoh.
Browsing: Shrewsbury
The 33-year-old was a free agent after leaving Burnley at the end of the 2019/20 season.
Shrewsbury Town rallied for a shock 2-2 draw against Liverpool in the FA Cup fourth round on Sunday, forcing a replay of the match to determine which team will advance.
They had fielded a virtual youth side and still beat Everton in the FA Cup third round on Sunday, while Bristol City and Shrewsbury drew 1-1 on Saturday.
Stoke have sacked manager Gary Rowett only eight months after recruiting him from Derby.