Freddie Piquionne opened the scoring for the Hammers, on his return to the starting line-up, after only 9 minutes.
Some great work from Captain Kevin Nolan and Mark Noble saw Nolan feed Matty Taylor, himself just returning from injury. Taylor then crossed for Piquionne to head home from close range to give the Hammers the start they were looking for.
The Hammers then had the best of the first half before soaking up some pressure from the home side in the second half.
Carlton Cole replaced Piquionne on 70 minutes and then went on to secure the game in the final minutes of injury time with some opportunistic work capitalising on a mistake from Matthew Bates.
The victory makes it seven wins from ten games on the road this season for the Hammers and only the first home defeat for Middlesbrough for almost a whole calendar year.