Robert Snodgrass gave the Canaries a half-time lead, a Ben Foster howler gifted Grant Holt a second, the third was an own goal from former Ipswich defender Gareth McAuley and Jonny Howson scored a spectacular late fourth.
"I thought we were excellent from the first minute right through to the 93rd minute," said Hughton, following a third win in 20 games.
"Incredibly relieved. We've embarked on a tough season, we've had some good periods in that season.
"We've found it difficult since Christmas to get the right formulas to win us football matches.
"On a day that it really counted, it was arguably our best performance of the season."
Hughton had a fitful night's sleep ahead of the match and hopes for another tonight in celebration of survival, which was his remit on his appointment last June.
"It means absolutely everything," said former Newcastle and Birmingham boss Hughton.
"I must admit I didn't get too much sleep last night and hopefully I won't get a lot of sleep tonight either.
"I'm not the most outwardly emotional person, but I'm chewing up inside.
"It's certainly my most satisfying [achievement], because of the pressure of the day.
"For this club, for this moment and the pressure on this game, this would probably be my proudest moment."
Hughton was able to savour the final 28 minutes after Foster's decisive error.
The England goalkeeper met Wes Hoolahan's prod forward with a mis-kick which allowed Holt to walk the ball in.
"Once the second one went in, we started to believe that it could be our day," said Hughton, who felt his side were due some luck.
John Ruddy returned from a five-month absence due to a thigh injury in goal and was untroubled, while Snodgrass, Holt and Hoolahan impressed.
Hughton was happy to sing the praises of a number of his players, but West Brom boss Steve Clarke was unable to explain his side's failings.
He said: "We've been terrific this season, today we were the opposite. We were really poor.
"It's a blow to us because that's not a normal performance for West Bromwich Albion.
"Today we were nowhere near it. It was Norwich's day, not ours."
Clarke refused to criticise Foster.
"It's a mistake," Clarke said.
"He knows it's a mistake. He didn't do it on purpose. And it was pivotal in the game.
"At 1-0 there was still the nervousness and the tension around the stadium. At 2-0 it released the pressure and they ran away with the game at the end."
Peter Odemwingie came on as a substitute late on after a second half of the season in which his Twitter tirades have been an unwanted distraction.
Clarke expects the Nigeria forward to leave this summer.
The West Brom boss said: "His future will be decided in the summer. I don't think he'll be here next season."