Didier Drogba's first-half goal takes Chelsea on to 74 points from 29 matches with Manchester United in second place on 63 and champions Arsenal a further two points adrift in third.
With nine games to play, however, Chelsea captain John Terry said there was still a long way to go after a hard-fought win in a match rearranged because of their League Cup final appearance.
"Man United are pushing us all the way, Arsenal are still there, so all we can do is keep winning our games and putting pressure on those two," the England defender told Sky Sports.
"We still need a few wins and hopefully we can do that with performances like that (tonight)," he added.
Chelsea, who commemorated the centenary of their foundation with a celebrity-studded dinner on Monday night, dominated from the start as they put the visitors under constant pressure.
They were rewarded after 26 minutes when striker Drogba tucked the ball home from eight metres after Damien Duff lost his marker down the left and cut back a precise low cross.
50 GOALS
It was the 50th goal West Brom have conceded in the Premier League this season and only bottom club Norwich City (58) have let in more as the pair struggle to avoid relegation.
Drogba should have scored a second goal just after the hour mark when he turned defender Thomas Gaardsoe outside the penalty area but flashed his low shot wide of Russell Hoult's far post.
Ten minutes later the Ivory Coast forward had another clear chance to increase Chelsea's lead but somehow managed to head the ball wide of the post from an unmarked position.
West Brom battled gamely and a Kanu volley moments later was headed over by the excellent Robert Huth, but the Midlands side rarely looked capable of getting back on level terms.
"We have got to take the good points out of the game," said West Brom manager Bryan Robson. "We were playing one of the best teams in Europe so we've got to take that into the Charlton game on Saturday," he added, referring to his team's visit to The Valley.
The loss leaves Albion second from bottom just a point above Norwich. Their haul of 21 points means they are five away from the position of safety occupied by Crystal Palace.
