City suffer sixth defeat on the spin
Toby Syme made his Under-21s debut at full back and Cameron Norman, who is on loan at Woking but allowed to play for the Canaries under the terms of the deal, returned for Dmitri Halajko's side.
Halajko reflected on a difficult afternoon, telling canaries.co.uk: "We're really disappointed in ourselves and in our performance, but Middlesbrough took advantage of that.
"There were spells where we were competitive, but in the second half we've just fallen away, and it's not good enough from us and we need to get better.
"The good thing about football is that there are always more fixtures around the corner and there's no better opportunity than facing Manchester United at Carrow Road on Monday."
In a first half devoid of chances, it was Middlesbrough who took advantage shortly before half time, as Fewster tapped in from close range after Jake Kean had saved the initial effort.
That lead was then doubled ten minutes into the second half; some trickery from Harry Chapman helped him to release Fewster, and he fired past Kean in the penalty area.
The striker should have completed his hat-trick a few minutes later when sent through on goal, but he could only poke the ball narrowly wide of the target.
Glenn Middleton was unlucky to see his effort rattle the crossbar as City sought a route back into the game, but Fewster secured the match ball moments later as he ran through the Canaries' defence and hit a low drive past Kean and into the net.
Middlesbrough then netted twice in quick succession as Junior Mondal took advantage of a slip to surge through the middle of the park and fire beyond Kean, before a quickly-taken free kick completed the scoring. A short pass found Joao Morelli, who rifled a powerful effort into the top corner to make it 5-0 to the visitors.
FULL-TIME: Norwich City 0-5 Middlesbrough
NORWICH CITY: Kean; Syme, Norman, Efete (c), Lewis; Grant, McGrandles, King (McIntosh 84); Eaton-Collins (Ashley Seal 78), Loza, Middleton. Subs not used: Killip (GK), Ellesley.