Despite being ranked among the promotion favourites, Darren Moore's side took only one point from their opening two games.
But Albion, relegated from the Premier League last season, finally kick-started their challenge with a powerful display at Carrow Road.
Striker Jay Rodriguez showed why Burnley were keen to sign him as he bagged a brace after Jordan Rhodes had put Norwich ahead.
Harvey Barnes scored his second goal for his new side to make it 3-1 but Norwich kept within contact.
Teemu Pukki pulled one back before Hal Robson-Kanu had scored West Brom's fourth.
Grant Hanley netted Norwich's third, but the hosts could not find a leveller.
Swansea City came down along with Albion, but they have maximum points after two Championship games thanks to a 1-0 victory over Preston North End.
Ollie McBurnie saw an early penalty saved by Declan Rudd but Jay Fulton netted the winner in the 32nd minute.
Leeds boss Marcelo Bielsa maintained his impressive start as the Yorkshire club thrashed Frank Lampard's Derby 4-1 at the iPro Stadium.
Following a 3-1 win over Stoke last weekend, Leeds were in fine form again as former Argentina and Marseille coach Bielsa won his battle with ex-Chelsea star Lampard, who was taking charge of the Rams at home for the first time.
Lampard had celebrated Derby's dramatic last-minute winner at Reading on his debut, but this was a chastening experience for the former England midfielder.
Mat Klich put Leeds ahead with a long-range strike in the fifth minute before Tom Lawrence equalised seven minutes later.
Kemar Roofe restored Leeds' advantage midway through the half and the striker netted again after the interval before Ezgjan Alioski sealed the rout.
Middlesbrough won 1-0 against 10-man Birmingham City, who had Craig Gardner sent off, thanks to Britt Assombalonga's early goal.
Aston Villa are expected to feature in the promotion chase after losing in the play-off final against Fulham last term.
They have made a solid start to the season and Birkir Bjarnason popped up to secure a 3-2 win over Wigan Athletic four minutes into stoppage time.
Sheffield United claimed their first points in their third game with a 2-1 win over Queens Park Rangers.
Reading are still searching for their first points after losing 1-0 to Hillal Soudani's goal for Nottingham Forest.
Jamie Paterson scored nine minutes from time to earn a 2-2 draw for Bristol City against Bolton Wanderers.
Rotherham United beat Ipswich Town 1-0, while Sheffield Wednesday drew 1-1 with Hull City and Blackburn Rovers were held to a 0-0 draw by Millwall.
Stoke City, relegated from the top flight last season, are still searching for their first win after Ollie Watkins cancelled out Benik Afobe's opener in a 1-1 draw against Brentford.