Michael Laudrup's side follow up their goalless draw against Liverpool on Sunday by taking all three points to put a halt to Steve Clarke’s team’s superb recent run of results
All the goals came in the first half, in which the Swans dazzled. Michu fired in the first from close range before Wayne Routledge struck twice, while Romelu Lukaku's reply was not enough to provoke a comeback.
Michael Laudrup opted to make one change from the side that were held to a goalless draw against Liverpool on Sunday, bringing in Ki Sung-Yueng for Itay Shechter with Michu moving up the pitch to play as their lone frontman.
As for the visitors, Steve Clarke made two changes from the starting XI that won 4-2 away to Sunderland in their last outing - with Romelu Lukaku and Youssuf Mulumbu coming in for Zoltan Gera and Shane Long.
The home side were rewarded for their bright start in the ninth minute when top scorer Michu got himself on the scoresheet. Nathan Dyer got forward well before whipping in a cross from the right which Pablo Hernandez did well to lay off first time to his fellow Spaniard, who applied the finish from close range.
The Welsh outfit doubled their lead three minutes later - this time through ex-Tottenham wideman Routledge. The stylish Hernandez was again involved in the build-up, this time forcing himself to the byeline before picking out his team-mate. His attempt deflected off Baggies defender Gareth McAuley and past a helpless Boaz Myhill.
The Swans added a third just over five minutes before half-time. Dyer played it to young full-back Ben Davies, who picked out Hernandez with a neat ball. The Spaniard continued his impressive evening by crossing to Routledge, who applied the finish to grab his second.
West Brom headed into the match having won their last four matches and restored some hope of continuing that streak thanks to the final piece of action in the first half. Ki failed to deal with Chris Brunt's corner and on-loan Chelsea striker Lukaku pounced to grab his second goal in as many matches.
Neither side managed to dominate the early stages of the second period, with a rash Lukaku effort the only chance to fall to either team in the opening minutes as they searched for another goal.
The hosts sprung to life in the 72nd minute, when Hernandez did well to pick out Michu, whose header hit the target but was comfortably saved by Myhill.
The visitors' keeper was again called into action two minutes later when Michu forced him to make another solid stop from his long-range attempt.
As much as they tried, West Brom failed to get themselves on the scoresheet again with the home side content to keep their lead intact.
Next up for Swansea is a trip to the Emirates Stadium to face Arsenal, while West Brom will be looking to get back to winning ways when they host Stoke City.