Hooper's 13th-minute strike - his second goal in three matches - and Fer's last-minute goal ended a wretched run of results on the road for Chris Hughton's side, who had conceded 18 goals in those four defeats.
The ex-Celtic forward took his goal well, sending a finish across Boaz Myhill after being set up by Fer, before the Dutchman made the game safe in the final minute, cutting inside from the left to shoot low into the net.
West Brom had thrown on Shane Long and Saido Berahino for the second half but the hosts, and Stephane Sessegnon in particular, were guilty of wasting chances to bring themselves back into the game.
Both sides made a number of changes following midweek defeats, the hosts showing five alterations and Norwich three, with Hooper among those to return to the side.
And he put Norwich in front after 13 minutes, planting the ball into the bottom left hand corner from 18 yards after being picked out by Fer.
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 tested 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 half-time, 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 levelled matters five minutes later, the Benin international bursting through the middle of the Norwich defence before placing his shot wide of the post with just Ruddy to beat 15 yards out.
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 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 they were unable to find a way past a resolute Norwich backline, and Fer fired a low shot beyond Myhill from 18 yards to extend West Brom's winless run to six matches.
