Morgan Amalfitano's first-half strike was enough to see the Baggies to victory at Carrow Road, as they moved up to 16th in the Premier League standings.
Norwich launched a spirited comeback in the second half but West Brom's defensive ranks stood tall as they leapfrogged their opponents, courtesy of a superior goal difference.
After being denied victory by a 95th-minute equaliser against Cardiff City last weekend, Mel was delighted to see his side take all three points at Carrow Road.
"I thought both teams really competed," he told Sky Sports.
"But today we was very good for us. It was a performance that made us proud.
"I think last week the team played well but only took one point. Today we were away but still picked up all the points."
After taking the lead 16 minutes into the match, West Brom defended with 11 men behind the ball for the majority and Spanish coach Mel praised the unity of his side.
"We were all together today," he added. "It is important that we stay together for the future of the team."
There were jubilant scenes among the travelling supporters at full time and Mel hailed support received by his side as the relegation battle rumbles on.
"This win is for the fans, we are all together, West Brom is a family," he said.
Albion host Tottenham at The Hawthorns next weekend before a testing trip to the Etihad Stadium to face title-chasing Manchester City.