After winning the toss and electing to bat, Dan Humes (37) and Peter Clark (34) shared a half-century stand for the first wicket.
But wickets then fell at regular intervals as Shrewsbury were dismissed for 182.
In reply, Smethwick were reduced to 41-3 with George Garrett bagging all three wickets. But the home side then hit back, losing one more wicket as they reached their victory total in the 42nd over.
The defeat leaves Shrewsbury rock bottom of the table.
Shifnal are sitting fifth after securing a 77-run success at home to Ombersley.
Chad Brandrick top scored as Shifnal posted 247-4 from 55 overs. Robbie Clarke (48 not out), Xavier Clarke (38) and James Sookias (36) provided solid support.
Shaun Lorimer (5-43) and Alex Renton (3-45) then led the victory charge with the ball as Ombersley were dismissed for 170.
Wem slipped down to third place in Premier Division after visiting Kenilworth Wardens triumphed by three wickets to climb above them into second spot.
Batting first, Wem were handily placed on 118-2 but the loss of Mohit Kale, run out for 59, checked their progress as they were all out for 209 in the 55th over.
Some disciplined bowling made runs hard to come by for Wardens early on in their reply, but a solid 66 from Ali Zaryab Asif, plus 46 not out from Andrew Leering and an unbeaten 30 from Josh Baker saw them home after 53 overs.
Bridgnorth are one place above the drop zone after tasting defeat at home to Himley.
Former Shropshire and Shrewsbury opener Ollie Westbury struck 100 in Himley's total of 278-6 – skipper Sam Whitney picked up 4-69 for the hosts.
Bridgnorth them moved to 104-2 in reply but couldn't kick on for victory as they were dismissed with just two balls of their innings remaining for 229.
Dave Exall top scored with 59 while Tom Weston made 41 and Ben Lees 39.
A stunning display from Shropshire's Charlie Home condemned Oswestry to defeat at Wolverhampton.
Wolves were 22-3 but a fourth-wicket stand of 193 between Will Nield (114) and Home (90) helped them to recover to 268-8.
Home then took centre stage with the ball, ripping through the Oswestry line up to finish with 7-33 as they were rolled over for 132. Ryan Lockley made 58 and Warrick Fynn 34.