On this evidence they could be in for another season of struggle, although Blackburn do not look as if they will fare much better.
Devoid of ideas and inspiration in the first half, the home team failed to impose themselves on the game until Graeme Souness sent on Turkish playmaker Tugay at half-time.
Almost immediately, Rovers were pepped up and got their reward when veteran centre-back Craig Short headed home on 70 minutes.
By that time Blackburn were already behind to Neil Clement's fiercely-struck free-kick, which crashed off the wall and beyond the stranded Brad Friedel in the 33rd minute, to hand the boisterous Albion the lead.
This may have been the first day of the new Premiership season but there was no sparkle from either side in the opening period, as they toiled to little effect.
Souness' bizarre tactics had not helped the flow of the game. His decision to employ Dominic Matteo in front of his back four left a gaping hole down the right-hand side - one which they struggled to plug throughout the first half.
Indeed, the only magic on show came from the twinkling toes of West Brom forward Nwankwo Kanu, whose languid style always threatened to carve open the Rovers defence.
Aside from their new Nigerian Albion's only threat came from set pieces, so it came as little surprise when that proved their route to the opener.
After a Matteo foul on Geoff Horsfield 30 yards out, Clement stepped up to take the free-kick. An ex-target of Souness, the West Brom captain smashed his effort against the home wall and it looped away from Friedel and into the goal.
The Rovers fans were stunned. Having beaten one of last year's newly-promoted sides, Wolves, 5-1 on the opening day, going behind to West Brom was not in the script.
It was not until Souness changed things around at half-time, throwing on Tugay and striker Paul Dickov that the home team began to pose a genuine threat.
Even so, Friedel's alertness rescued his side in the 50th minute after Lorenzo Amoruso's short back-pass let Kanu in - the American goalkeeper racing out of his area and managing to dispossess the former Arsenal man.
After Dickov's penalty appeal fell on deaf ears, Rovers got the equaliser when their ageing centre-back Short lumbered up from the back to meet Jonathan Stead's cross with a terrific header into the corner of Russell Hoult's goal.
Brett Emerton and then Paul Robinson at the other end squandered chances to win it in the closing stages before Barry Ferguson's whipped cross flew inches wide of the post.
It finished a point apiece, and Albion are already ahead of their last Premiership campaign when they lost their opening three games.
It will take better performances from both these sides though for them to clamber away from the relegation battle this season.
Man of the MatchNigerian forward Nwankwo Kanu showed the kind of form that persuaded Ajax, Inter Milan and Arsenal to sign him earlier in his career. He demonstrated an array of skills so badly lacking in the rest of the players on show and gave the Baggies' travelling faithful something to cheer about.