Robert Snodgrass gave the Canaries a half-time lead before a Ben Foster howler gifted Grant Holt the second and former Ipswich defender Gareth McAuley's own goal prompted Delia Smith to dance with delight.
The Baggies were woeful and Jonny Howson scored a spectacular late fourth as Chris Hughton's men claimed a third win in 20 Premier League games to make certain of their top-flight status ahead of next week's final day trip to Manchester City.
FA Cup winners Wigan, who play Arsenal on Tuesday, meet Aston Villa on the final day of the season, meaning at least one of the sides below Norwich will drop points this term.
Unlike their hosts, West Brom had little to play for, with eighth or ninth place their only possible finishing position.
Steve Clarke made five changes for the visitors, while Hughton made a solitary, but significant change following the defeat to Villa.
John Ruddy, back in goal for the first time since November following a thigh injury, was the quieter of the England goalkeepers early on, but Norwich did not test Foster despite a lively start.
Wes Hoolahan's movement was a particular nuisance for the Baggies and the industry of Snodgrass was troublesome, too. Snodgrass created an opportunity for the Canaries as the ball broke for Anthony Pilkington, who fired a left-footed shot Foster could only parry away.
A corner followed which the visitors failed to adequately clear before going behind. Holt crossed, Ryan Bennett won a header down towards Hoolahan, whose attempt to turn the ball in was saved by Foster.
The ball ricocheted into the left side of the area and Snodgrass swept a left-footed effort into the roof of the net for his seventh of the season.
Norwich's attempts to build on their advantage floundered as they frequently relinquished possession, but fortunately for the hosts, Albion were lacklustre and appeared to have adopted the attitude of some of their fans, who brought beach balls and other holiday inflatables to Norfolk.
Hoolahan tried to provide a spark for City and saw his dipping shot from 30 yards tipped over by Foster.
Snodgrass' set-piece resulted in a melee and the ball hit Jonas Olsson on the arm, but referee Howard Webb adjudged it was ball-to-hand contact and rejected penalty appeals.
Clarke reacted to his side's insipid first-half showing by introducing Billy Jones for Reid and fit-again captain Chris Brunt for Markus Rosenberg, but it made little difference early on.
Olsson survived another handball appeal when Pilkington failed to connect with Holt's knockdown from a Russell Martin free-kick before the Baggies defender hauled down Holt and was booked.
Snodgrass then hesitated when through on goal and Olsson recovered to nick the ball.Foster spilled a Bradley Johnson cross and Holt could not quite get over a header from a Snodgrass cross as Norwich kept up the pressure.
The hosts had the second their play deserved after 62 minutes - and it was a gift from Foster.
The goalkeeper met Hoolahan's prod forward with a mis-kick which allowed Holt to walk the ball in, igniting chants of "We are staying up".
Delight turned to jubilation when Norwich had their third as McAuley, under pressure from Bennett, turned a Snodgrass set-piece into his own net.
Foster saved a Pilkington shot which appeared destined for the bottom corner before Holt was given an ovation as he made way of three minutes from time.
There was still time for a fourth as Howson cut in from the right, received a return pass from Holt's replacement Luciano Becchio, and found the top corner.