It was his quick-thinking from a corner that helped set up Blackpool's opener, playing a corner short to Stephen Crainey, whose centre was only cleared to Vaughan on the edge of the box.
Midfielder Vaughan took a touch on his right foot to move it onto his left before curling the ball beyond Myhill, who was making his first Premier League start for West Brom in place of the dropped Scott Carson.
Campbell then went down under an innocuous challenge in the box, but his appeal for a penalty was waved away by referee Stuart Attwell.
West Brom began to get a foothold in the game with Jerome Thomas looking particularly dangerous down the left.
He twice crossed for Chris Brunt but the Albion skipper volleyed one effort wide while his second was well-blocked by Crainey.
Luke Varney reminded Albion that Blackpool were still a threat though.
He chased a ball down the line that Gabriel Tamas had given up as going out, before cutting inside and firing wastefully over from 20 yards.
But Albion's pressure deserved a goal and top scorer Odemwingie duly obliged.
He collected a perfectly clipped centre from Graham Dorrans and, with the Blackpool defenders appealing for offside, he beat Richard Kingson with a low strike to score his seventh of the season.
The second-half began in similar fashion to the first with Blackpool in the ascendancy and Campbell dragging a shot wide.
This time, the striker, who had scored five goals in his previous five games, was one-on-one with Myhill after being played in by an exquisite pass from Adam, but he pulled his effort past the right-hand upright.
Blackpool were immediately made to pay.
Thomas jinked into the box and Kingson could only palm the Albion winger's centre into the path of Morrison who nudged the ball home from close range.
Morrison should have made it 3-1 moments later, but Kingson saved with his legs to atone for his earlier error and the Ghanaian international keeper then closed down Odemwingie and pulled off another fine stop.
Ref should have awarded penalty - Holloway
The chances continued to come, and Nigerian striker Odemwingie unselfishly played in Morrison, but the midfielder scooped his effort over with only Kingson to beat.
This time, the Baggies were made to pay for their profligacy in front of goal.
Vaughan found Matt Phillips out on the right wing with a measured pass and his first-time centre was met by Taylor-Fletcher who side-footed the low cross into the net to bring Blackpool level.
However, the home side refused to settle for the point and Odemwingie beat Craig Cathcart to a long ball over the top before volleying in from 16 yards.
There was still time for Blackpool but Campbell missed his third chance of the afternoon from close range and as the ball bounced free, Brett Ormerod poked wide, but it would have been a harsh end to the game had the Tangerines grabbed a second equaliser.
West Brom manager Roberto di Matteo: "It was an exciting game for the fans and neutrals.
"There were so many chances and we are just pleased we got the win. Every win is a big win and because we have not won for a few weeks, it is even better.
"It was a rollercoaster of emotions and it wasn't our best game of the season but we're pleased to get three points."
Blackpool manager Ian Holloway: "It was two good teams having a go at each other and it could have been 6-5, unfortunately we came out on the wrong end of it.
"It changed on what looked a blatant penalty when we were leading 1-0 I haven't had hindsight of seeing it again, but I'm saying it as I saw it.
"Then one ball over the top does us. We should do better but such is life."
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