Chris Hughton's side was on the receiving end of a 5-1 loss against Liverpool last time out, but responded with a solid display at the Hawthorns that pushes it up the table.
Gary Hooper gave the visitors an early lead, latching onto Leroy Fer's through-ball and firing the ball into the bottom corner, before the Dutchman wrapped up the win late on.
Both sides made a number of changes following midweek defeats, the hosts showing five alterations and Norwich three, with the ex-Celtic forward among those to return to the side.
|VIEW FROM THE HAWTHORNS
|By Tom Davis
What a victory for Norwich but West Brom will be bitterly disappointed. It was such a timid performance from the Baggies when they should have entered this game all guns blazing against a Norwich team which, on the evidence of recent form, might spend the season clawing away from the relegation places.
But the Canaries have given themselves a massive three points today with a terrific performance both in defense and attack. It had gutsy tackles, strong wing play and classic counterattacking moves, but Steve Clarke saw his players give little in return – not to mention the catalog of misses in the second half.
West Brom responded strongly, Youssouf Mulumbu firing an effort straight at John Ruddy after combining neatly with Morgan Amalfitano on the edge of the area in the 18th minute.
Nathan Redmond then tested Boaz Myhill with an awkwardly dipping free kick nine minutes later, and Ruddy palmed Victor Anichebe's powerful shot over the crossbar 10 minutes before the break.
Steve Clarke made an attacking double substitution at halftime, Berahino and Long replacing Amalfitano and Liam Ridgewell, and the hosts felt they could have been awarded a penalty a minute after the restart when Sessegnon's close-range effort appeared to strike a combination of Martin Olsson's chest and right arm.
Sessegnon ought to have leveled matters five minutes later, the Benin international bursting through the middle of the Norwich defense before placing his shot wide of the post with just Ruddy to beat.
Jonny Howson curled his shot a yard over Myhill's bar in the 63rd minute, before Sessegnon was wasteful again a minute later, firing straight at the legs of Ruddy after Olsson's poor clearance fell to him inside the six-yard box.
The hosts, ruing their profligacy, continued to press, Long volleying straight into the arms of a grateful Ruddy before Anichebe headed Billy Jones' cross wide of goal.
The closing stages were dominated by West Brom, but it was unable to find a way past a resolute Norwich backline, and it was the Canaries who bagged a killer second goal.
Inside the final minute, Fer cut in from the left and fired a low shot beyond Myhill from 18 yards to extend West Brom's winless run to six matches, and end a wretched run of results on the road for Hughton's side, which had conceded 18 goals in those four defeats.