Middlesbrough gained some sweet revenge after crashing to a 1-0 defeat at the Hawthorns in November.
The win extended Boro's unbeaten run to seven games and encouraged hopes of the team finishing the season in style.
The target is to achieve the Teesside club's best points total in the Premier League.
Eight points from the last six games would beat the previous best of 52.
Boro boss Steve McClaren was pleased with the overall performance of his team.
The former number two at Manchester United said: "It was a little frustrating in the first half.
"We should have been more goals up. You began to wonder in the second half whether it was going to be one of those days.
"I thought our attacking play at times was breathtaking, although we lacked that final finish.
"We missed several opportunities. Hopefully we are saving a few of those chances for future games." McClaren has been cautious all season to discuss the prospect of European football coming to the Riverside Stadium and he was again non-commital over that prospect.
"I don't know how many points will be required for Europe. I'm not really focusing on that. You have to concentrate on each game and make sure you perform. We want a good end of the season." For West Brom, though, a quick return to the First Division is inevitable.
"With a lack of financial clout, the Baggies have struggled to score goals all season and there was never any real prospect of the Midlands team getting out of the rut in this game.
The Albion supporters, however, showed their loyalty to manager Gary Megson by chanting his name in the second half.
Albion fans know Megson has had a difficult task without the financial resources to mix it with the big boys of the Premiership.
Megson, however, said that relegation would hurt because the Premier League was the only place to play football.
The Albion boss had reassuring words for fans who gave his side tremendous encouragement.
"We won't have to go into administration. We won't have to sell every player." he added.
After explaining the financial pros and cons he joked: "I am talking like a bank manager," as he left the press room.
Middlesbrough were full value for their win and could easily have doubled the scoreline if they had taken their chances.
Malcolm Christie gave Boro a first-half lead with his third goal since his transfer window move from Derby County. The young striker looked a fine buy.
Jonathan Greening got some reward for his wholehearted display by increasing the lead after 76 minutes after combining with fans' idol Juninho.
Second-half substitute Szilard Nemeth rounded it all off with a third goal just three minutes from time.