An early Saido Berahino goal proved to be enough for the Baggies to edge closer to safety, and manager Mel was keen to praise the young forward and the supporters after the final whistle.
"I am extremely proud of the players," the Spaniard told the club's official website. "They worked very hard to achieve this win. The atmosphere the fans generated really helped us.
"The fans have shown since I arrived they are best in league. I have to thank them because they really did help us get over line today.
"It was very important that Saido played well and scored. I thought it would be a good game for him and it paid off."
West Brom have moved up to 15th in the table thanks to the win.