Middlesbrough avoided an FA Cup shock as Marvin Emnes' strike ensured Shrewsbury's impressive performance proved in vain.
Making their first appearance in the third round for nine years, the Shrews were dominant in the first half.
Lionel Ainsworth was guilty of firing their best chance wide on 30 minutes.
But Boro scored the only goal on the stroke of half-time when Emnes showed neat control to bring down Malaury Martin's cross before slotting home.
Tony Mowbray's side showed resilience to close out the game in the second period and Emnes could have doubled their advantage late on.
The hosts enjoyed the better of the opening exchanges, although Shrewsbury soon rallied and created the first clear opportunity.
Taking advantage of poor defending, Mark Wright surged forward and struck inches wide of the post.
That spurred the visitors on, with Terry Gornell forcing Jason Steele into a save before Martin narrowly missed the target.
Ainsworth spurned Shrewsbury's best opportunity when he placed his shot wide with the goal gaping.
The Championship side went in front just before the break, Martin sending a ball towards the back post where Dutchman Emnes beat Chris Neal.
Boro pressed immediately after the interval as Bart Ogbeche forced a save from Neal with a fine volley.
But the Shrews came back into it and Marvin Morgan missed the target with a decent chance before Matt Richards forced another save from Steele.
Emnes could have finished the game off but shot wide.
The away side continued to create the better chances, with Wright and Terry Gornell missing from close range.
Morgan forced a fine save from substitute keeper Danny Coyne in the dying seconds as Boro held on.
Middlesbrough boss Tony Mowbray tells BBC Tees: "There's no easy games in football whoever you play and the FA Cup is littered with giantkillings over the last 100 years.
"We should just be happy to have won the game.
"We have total respect that they're having a decent season in their own division, and it wasn't an easy or comfortable day and yet thankfully we kept a clean sheet."
Shrewsbury boss Graham Turner: "I think it is fair to say we are bitterly disappointed that we didn't get something.
"I think we deserved at least a draw and to take them back to our place in a replay.
"We should have had the ball in the back of the net a few times. We had our opportunities."