Both sides had chances in the first half, while the visitors were aggrieved not to be awarded a penalty following a handball from Emmanuel Adebayor.
However, Morrison's header with just over 15 minutes to spare was enough for them to climb off the bottom of the table, leaving Spurs without a win in their last three Premier League outings.
Heres, Sports Mole takes a closer look at the action.
On target: 1
On target: 4
Was the result fair? Tottenham will argue not, given their superior possession, but, on balance, West Brom probably did deserve the three points. They were quick out of the blocks and ran at the Spurs back four throughout the afternoon. They were also unlucky not the break the deadlock in the first half when they were denied what looked like a stonewall penalty, and had a goal ruled out for offside.
Spurs did not quite seem to hit their top pace this afternoon, struggling to get the better of a well-organised West Brom back four. In the first half they relied too heavily on Emmanuel Adebayor when going forward, while a string of errors at the back constantly gifted West Brom corners and shots, ultimately resulting in Morrison's goal after the break.
West Brom's performance
The visitors never seemed to take a break as they relentlessly chased the ball, put their opponents under pressure constantly and worked well as a team. Despite their missed chances in the first half, and some misfortune with the penalty incident, West Brom never let their heads drop. While some poor defending from Tottenham ultimately allowed West Brom to get their goal, it was a well-deserved win for Alan Irvine's men.
Sports Mole's man of the match
Joleon Lescott: Having missed the start of the season with an injury, Joleon Lescott would have been forgiven for looking a little rusty on his debut for West Bromwich Albion, but he was superb at the back for the visitors today, making countless blocks, never giving up the chase to ultimately ensure that Ben Foster only had to make one real save, and even getting forward for a couple of shots. Now that he is healthy again, Lescott could make a real contribution for West Brom this season if he plays like that in every match.
There are a few candidates from the Spurs team, but this one actually has to go to Craig Gardner, who managed to block his own teammate's shot in the first half. Lescott unleashed a powerful volley early on which seemed to be heading for the goal, but the midfielder did not see the ball coming and accidentally cleared it from the Spurs box to deny the defender a goal on his debut.
The only really contentious decision for Kevin Friend to make was when West Brom appealed for a penalty shortly before half time. In real time, it did not look like a problem as Adebayor cleared Craig Dawson's effort, but replays clearly showed that it was handball by the striker. While Friend does not get the benefit of such replays, he was in a good position and probably should have done better.
Tottenham: Spurs host Nottingham Forest in the League Cup in midweek before facing a trip to the Emirates to take on North London rivals Arsenal in their next Premier League outing.
West Brom: West Brom will also be in cup action on Wednesday, facing Hull City, before hosting Burnley in the league next Sunday.