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.
FA Cup winners Wigan meet Aston Villa on the final day of the season, meaning at least one of the sides below Norwich will drop points.
John Ruddy, back in goal for the first time since November, was the quieter of the England goalkeepers early on, but Norwich did not test Foster despite a lively start.
But their failure to deal with a Norwich corner saw them fall behind. Wes Hoolahan's attempt to turn the ball in was saved by Foster but it ricocheted to Snodgrass swept a left-footed effort into the roof of the net.
Hoolahan tried to provide a spark for City and saw his dipping shot from 30 yards tipped over by Foster. The former Manchester United keeper then 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 in the 62nd minute - 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 the ball into his own net.
Foster saved a Anthony Pilkington shot which appeared destined for the bottom corner but there was still time for a fourth as Howson found the top corner.