Shrewsbury set up an FA Cup fourth-round clash at home to Liverpool as Aaron Pierre's fine late goal earned them a 1-0 win over Bristol City.
The League One side secured a memorable meeting with the unbeaten Premier League leaders thanks to Pierre's low finish from outside the area in the 89th minute.
There were chances at both ends during a goalless first half, with City captain Josh Brownhill's early drive well saved by goalkeeper Joe Murphy.
Shrewsbury defender Pierre's long-range effort was just off target and home skipper Ollie Norburn's shot was deflected narrowly wide.
Nathan Baker went close with a header for the visitors before Famara Diedhiou lifted his shot over the bar when he was sent clear with Murphy to beat.
Shrewsbury striker Daniel Udoh forced a fine save from Daniel Bentley at the other end with a powerful effort from just outside the area.
Diedhiou fired wide for City early in the second half before home substitute Callum Lang's header was well kept out by Bentley.
With extra-time looming, Shrewsbury delivered the knockout blow in the 89th minute as Pierre picked out the bottom corner to allow his side to dream of an even bigger upset.
