The Finnish frontman, who scored twice for his country while on international duty, settled a scrappy game just before the hour mark when he took advantage of some rare poor defending from Boro to slot the ball home.
It was a well deserved win for the Canaries, who had only tasted victory once in the Championship before today, while Boro could have few complaints about the final result having created few chances all afternoon.
The Canaries gave as good as they got in a dull first half, although it was the visitors who created the one good opportunity.
Former Norwich midfielder Jonny Howson had a clear sight of goal after being picked out in the box by Britt Assombalonga and it took a good save from Tim Krul at his near post to keep the scores level.
The resulting corner from Stewart Downing struck the angle of upright and crossbar before being cleared - but those were rare moments of concern for the home defence.
Norwich had the bulk of possession but were kept largely at arm's length by a disciplined Boro defence.
It wasn't until seven minutes before the break that Daniel Farke's side finally got an effort on target, with Marco Stiepermann's long-range effort comfortable for keeper Darren Randolph.
The home side also started the second period on the front foot and Randolph was called into action after 56 minutes to save a low Alex Tettey drive from just outside the box.
But they deservedly went in front a couple of minutes later when a break into the area from young defender Max Aarons caught the visitors out and George Friend inadvertently played the ball into the path of Pukki, who poked the ball home from eight yards via a slight deflection.
It then needed a good block from Daniel Ayala to keep out a powerful shot from Onel Hernandez as Norwich pressed for a second.
Tony Pulis' side needed to show a lot more attacking intent if they were to get anything out of the game and they finally made Krul work again midway through the half when substitute Martin Braithwaite made himself some space in the box and fired goalwards.
There was a reprieve for Norwich 15 minutes from time when referee Andy Davies went back on his decision to show a second yellow card to Timm Klose.
The Swiss defender, who had already been booked, was penalised for hauling back Assombalonga and started to walk before the official consulted with his assistant and a free-kick was given the other way for offside.
Boro kept pressing but were unable to carve out another decent chance as the home side saw out the game with few alarms.
Boro boss Tony Pulis felt his side should have had a penalty just before Norwich went ahead - but had no complaints about the outcome.
He said: “Norwich were the better team but I think it was a clear penalty when Britt Assombalonga was brought down in the box early in the second half.
“It wasn’t given and they go up the other end and score a soft goal which had a lot to do with poor defending.
“We started the game okay and then dropped off after 20 minutes and we also started the second half poorly.
“It’s disappointing of course but this is the Championship and there’s always a chance you can get results like this. What we have got to do now is put it behind us and make sure we bounce back.”
There was a bizarre moment 15 minutes from time when Norwich defender Timm Klose was shown a second yellow card for bringing down Assombalonga when the striker was running in on goal, only for it to be withdrawn after consultation with his linesman, who had spotted an offside.
Pulis added: “That’s certainly something I have never seen before. The flag never went up at the time so I am not sure what happened there.
“Overall I thought the officials were poor - but as I said I don’t want to take anything away from Norwich.”