Early pressing from Boro almost brought a breakthrough when a well-worked free-kick picked out Robbie Tinkler inside the penalty area and a low shot was blocked.
Boro continued to enjoy more possession, but this was a slow burner and chances were rare.
As often happens in games such as these, the first shot on target counts and so it was as Junior Mondal was sent clear through the middle just right of centre and beat Ben Killip with a sweetly-struck low shot after 33 minutes.
A few minutes later it was nearly two when Callum Cooke crossed from deep out on the left, but a header from Carlos de Pena was inches off target.
It took just two minutes of the second half for Norwich to draw level as a foul by Matthew Elsdon conceded a penalty and Louis McIntosh drilled the ball straight down the middle.
It got worse for Boro on 56 when Benny Ashley-Seal made a well-timed run and shot low past Jo Fryer.
A fine cross whipped in from the left through the penalty area was only just in front of Jo Wheatley sliding in at the back post, then Robbie Tinkler sent a 25-yard shot just wide.
Tinkler went even closer a few minutes later when a header came back off a post.
There was a welcome return from injury for Arnel Jakupovic and lack of match sharpness cost him as a chance went begging not long after his introduction.
By then Boro had drawn level as Carlos de Pena had drilled home low from inside the penalty area to round off a controlled and well-constructed move.
Scorers Mondal 33, McIntosh 47 (pen), Ashley-Seal 56, De Pena 80.
Middlesbrough: Fryer; Johnson, McGhee, Morris, Elsdon, Kitching, Wheatley (Jakupovic 72), Tinkler, De Pena, Cooke (Capt.) (Morelli 84), Mondal. Subs: Pears (gk); McGoldrick, McAloon.
Norwich City: Killip (Capt.); Efete, Ramsay (Lewis 13), Grant, Godfrey, Crowe, Middleton, McGrandles (Higgs 79), Ashley-Seal, McIntosh, Jarvis (Sambu Mutala 74). Subs: Howell, Odusina.
Referee Andrew Miller
Boro Johnson 45, foul; De Pena 88, ungentlemanly conduct
City McIntosh, foul; Grant 88, ungentlemanly conduct
Conditions Cold and foggy