James Morrison initiated the move before Youssouf Mulumbu's one-touch ball released Amalfitano and the French playmaker drifted away from his defender before striking beyond a stretched John Ruddy.
The Norwich goalkeeper was called into action almost immediately following the restart as Stephane Sessegnon slid a neat ball through to Matej Vydra, who would have doubled the West Brom lead had it not been for a commanding save from Ruddy.
Ruddy's opposite number, Ben Foster protected West Brom's lead with an excellent save to deny Johan Elmander's header after a fine cross from Russell Martin was flicked on by Gary Hooper.
Chris Hughton's side tested the West Brom defensive ranks throughout the second period as they sought the elusive equaliser.
Robert Snodgrass also struck the woodwork with a stinging free-kick from 30 yards, after he was brought down Morrison.
Try as they may, Norwich could not break down a stoic West Brom defence, as the Baggies leapfrogged the Canaries in the Premier League standings.
Norwich made the brighter start before Johan Elmander crashed the ball high into the Barclay End after a deflected cross from Robert Snodgrass fell into his path on the edge of the West Brom penalty area.
It proved a costly miss, as the visitors went up the other end and swept into the lead on 16 minutes.
The ball was worked back inside from the left, and as full-back Martin Olsson slipped at the edge of the penalty area, Amalfitano skipped through before sliding a low shot across goal and into the far corner.
Norwich had not lost at Carrow Road in 2014 and needed a response to lift the silenced home faithful, clap-banners and all.
West Brom, though, remained comfortable in possession, determined to keep hold of their advantage.
It was almost 2-0 when a deep free-kick floated right through the Norwich penalty area and Jonas Olsson just failed to connect at the far post.
Norwich had Ruddy to thank when he blocked Vydra's close-range effort after the visitors broke quickly down the left on a counter following a corner.
It was then the turn of the West Brom keeper to produce a fabulous stop after 38 minutes as he made a superb reaction save to tip away a glancing header from Elmander after Gary Hooper's flick-on.
Loud boos greeted the half-time whistle, leaving manager Hughton in no doubt of what was needed in his team-talk.
The Canaries boss sent the same XI out for the restart and did at least get something of a response as West Brom were forced on to the back foot.
On 57 minutes, the ball dropped to Hooper at the back of a crowded six-yard box and the former Celtic striker was unfortunate to see his angled drive hit the woodwork.
Foster then turned a clever 25-yard floated free-kick from Snodgrass up on to the crossbar as finally Norwich asked some questions of the West Brom rearguard.
Hughton made a positive change on 64 minutes as England Under-21 winger Nathan Redmond replaced Wes Hoolahan.
Snodgrass cut into the right side of the box after good hold-up play by Hooper, but could only slice his shot wide.
Berahino replaced Vydra on 71 minutes and the forward was soon in the action as he dragged a half-hearted effort wide following a quick break down the left.
Berahino waltzed into the Norwich box in stoppage time, but his near post shot was saved by Ruddy.