Two goals in the space of six minutes gave United a comfortable lead before the half-time break as Joelinton's excellent strike broke the deadlock for the visitors at Carrow Road before the Brazilian, making his 100th Premier League appearance, doubled his and United's advantage with a simple tap-in.
Bruno Guimarães' stunning chip shortly after the restart, the midfielder's third goal in as many matches, added gloss to the scoreline to send Newcastle into ninth place of the English top-flight on 43 points.
Targett expressed his delight in helping Newcastle secure four consecutive Premier League wins for the first time since April 2018 along with recording back-to-back clean sheets.
"It was a really important win to end a tough week," the 26-year-old left-back told nufc.co.uk. "Three games in six days is always a big ask and I thought once we scored the first goal today, we looked really dominant and put ourselves in a good position.
"The three wins (against Leicester City, Crystal Palace and Norwich) are a good return and we'll make sure we recover well ahead of facing the big boys and see where we really are as a team. Hopefully, we can give them a good test.
"I don't think we came out of the traps until the first goal. Norwich put us under a lot of pressure and were definitely the better team before that. They wanted it a bit more at the start but once we scored, it changed the game and from then onwards, we took control of the match and caused them many problems.
"The timings of the goals kicks their confidence. They're fighting for their lives and need to win games so to get that second goal was massive and getting the third early on in the second-half killed it.
"We could have scored a few more goals but, overall, we're happy with the clean sheet and three goals away from home is always a good achievement in the Premier League.
"As defenders, we pride ourselves on clean sheets so to keep two in our last three games is a good achievement. We know how hard it is to keep them in the Premier League so it was a great job by the whole team."
The Eastleigh-born defender revealed he has relished his loan spell on Tyneside after joining from Aston Villa and, since his arrival in January, has been a mainstay in Newcastle's defence as the Magpies have impressively propelled themselves into the top-half of the division.
With United set to become the first Premier League side to avoid relegation despite failing to win in their opening 14 league matches, Targett is also aiming for the club to maintain their bright form of late in a bid to secure a remarkable top-ten finish.
"I'm loving it!" he added. "I'm playing with a smile on my face and when that happens, I think you can see by the performances on the pitch that I play at a consistent level and I'm glad I have came in, helped the team and we're kicking on to push up the table.
"It's been a massive turnaround. That takes a lot of hard work and what the manager has installed into us since the first day I joined. We've worked really hard to get where we are at the moment but there's still a few games left to play and we don't want to take our foot off the gas.
"Hopefully, we can finish in the top half of the table because that would be an unbelievable achievement, especially in that second-half of the season."
