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But it was rough on Blackpool who had fought their way back on to level terms through Scott Vernon's first goal of the season, after Ishmael Miller had given Albion a 22nd minute lead with his seventh goal of the season.
Simon Grayson's side will be wondering how they failed to win the game let alone even take a point against a nervy Albion team.
Albion dominated the opening half, but were given a stern examination in the second period.
The impressive Wes Hoolahan was denied by Albion goalkeeper Dean Kiely and a last ditch challenge from Martin Albrechtsen denied Vernon a second.
Kaspars Gorkss headed wide when well placed in the 59th minute and it needed a finger tip save from Kiely to push a drive from Keith Southern over the bar.
Failing to take their chances proved costly for Blackpool who were beaten for only the third time in the Championship this season.
Midfielder Morrison made them pay when Sherjill MacDonald's cross was deflected into his path and his 20-yard drive whistled past goalkeeper Paul Rauchubka.
It was a hard fought success for Albion who had looked set to cruise a far more comfortable win.
Albion laid siege to the Blackpool goal before Miller's strike with Morrison, Kevin Phillips and Jonathan Greening all going close before their pressure finally paid off.
Morrison was the creator, cutting in from the right wing and picking out Phillips. He then forced the ball into the path of Miller, whose low shot on the turn beat Rachubka at his near post.
But any hopes Albion had that Miller's strike would set them on the way to a comfortable victory were dashed just nine minutes later.
Once again, Albion's defensive frailties proved to be their undoing.
Bostjan Cesar, on his league debut, failed to win his tussle with Keigan Parker on the left-hand edge of the area.
Parker was able to force a low ball into the path of Vernon, who beat Albion left-back Paul Robinson to the ball before drilling his shot beyond Kiely.
Blackpool were content to soak up pressure and try and hit Albion on the break.
But sitting so deep threatened to cost them in the closing stages of the first half when Morrison was again denied by Rachubka, before Chris Brunt hit the bar with a cross shot.