Manchester United won a Premier League away game for the first time since February and would have beaten Norwich by more if not for two Tim Krul penalty saves.
United's two first-half goals came moments after outstanding Krul stops.
Scott McTominay slammed home the opener seconds after a stunning reaction save from the Canaries keeper to deny Anthony Martial from close range.
The video assistant referee (VAR) then controversially awarded United a penalty for a Ben Godfrey foul on Daniel James - with Krul stopping Marcus Rashford's kick.
But Rashford scored with United's next attack as he was left in acres of space by the Norwich defence.
United - who move up to seventh in the Premier league - were awarded a second penalty by VAR for a Todd Cantwell handball. This time Martial took it and went the other way, and again Krul guessed correctly.
The Canaries, who remain in the relegation zone, had a couple of chances but United wrapped the game up when Martial clipped the ball over Krul after a good passing move with Rashford.
Norwich scored a late consolation through substitute Onel Hernandez, who took the ball off McTominay before running at United's defence and shooting past David de Gea to becoming the first Cuban-born player to score a Premier League goal.
Krul and VAR catch the eye
In the first nine rounds of Premier League games this season no penalties were awarded by VAR with a seemingly high bar set for the "clear and obvious error" needed to overturn a referee's decision.
There have been four this weekend, including two at Carrow Road.
The first was highly controversial with Godfrey and James appearing to run into each other and referee Stuart Attwell changing his decision after consulting with the video team.
Krul appeared well off his line when he saved Martial's kick - but VAR in the Premier League does not check for goalkeepers' positions from penalties.
The second penalty was not contentious with the new handball laws with Cantwell's arms clearly high in the air as he blocked Fred's cross.
Martial became the third United player to fail from the spot in the league this season when Krul denied him.
He is the first goalkeeper to save two penalties in a Premier League game since fellow Dutchman Maarten Stekelenburg for Everton against Manchester City in October 2016.
Krul was brilliant throughout the game, making eight saves - including a remarkable stop to keep out Martial's header from point-blank range.
United continue improvement
This is a third decent result in a row for Manchester United as they climb away from the lower reaches of the league.
A draw against leaders Liverpool last Sunday was followed by a first away win since Paris St-Germain in March, when they beat Partizan Belgrade 1-0 on Thursday.
A Norwich team short on confidence was an ideal opponent to end their worst away run in the league since 1989.
McTominay, Aaron Wan-Bissaka, Martial and Rashford were all excellent - despite the latter two's penalty misses.
With their first chance, Andreas Pereira curled a shot just wide and then Martial thought his header was in from Rashford's flick-on - before Krul's brilliant save.
They led when Scotland midfielder McTominay curled home after Cantwell failed to clear Pereira's cross - United's 2,000th goal in the Premier League era.
Only Rashford has scored more league goals for United than McTominay's four since Ole Gunnar Solskjaer was named permanent manager in March.
Rashford and Martial's penalty misses mean United have failed to score with four of their last six Premier League spot-kicks.
But that did not dishearten them with Rashford running onto James' defence-splitting pass to stroke home a shot past Krul.
Their third was excellent. Rashford played a one-two with Martial - on his first league start since August - and then backheeled the ball back into the Frenchman's path for his deft finish over Krul.
It is far too early to read too much into one good week for United, but things are looking a lot more encouraging than they were in the preceding five-game winless run.