Despite a deceptively close scoreline, the home side dominated proceedings thanks to a poor showing from the visitors as a first half tap-in proved enough to secure the win
The hosts opened the scoring courtesy of a well-worked set-piece as Ba latched onto a David Luiz header across, and were largely untested for the remainder of the game by the lacklustre Baggies.
As was expected, Benitez made wholesale changes from his side's win over Middlesbrough in the FA Cup, as Cesar Azpilicueta, David Luiz, Ashley Cole, Frank Lampard, Eden Hazard, Juan Mata and Demba Ba all returned to the starting XI.
Steve Clarke, meanwhile, made two enforced changes as, with Romelu Lukaku unable to play against his parent club and captain Chris Brunt injured, Marc-Antoine Fortune and Graham Dorrans stepped in.
Chelsea had the better of the opening moments and were almost ahead after just three minutes as Oscar almost converted Ba's cross only to be denied by a smart Foster save.
Aside from a long-range Steven Reid free kick that Petr Cech tipped over, the home side managed to control the early stages as Oscar and Ba both missed further opportunities to break the deadlock within the opening half-an-hour.
Eventually though, Chelsea's goal arrived and it was courtesy of a cleverly-worked short corner. After a Luiz free kick was tipped adeptly wide by Foster, Oscar received the ball short from the ensuing set-piece and whipped a cross towards the back-post. Luiz was there to head the ball back across the goal, finding Ba on the edge of the six-yard box to put the home side deservedly ahead after 28 minutes.
After seeing out the remainder of a testing first half, the Baggies' second half continued in much the same vein as Chelsea dominated the opening 15 minutes, albeit without really testing Foster.
The game took a contentious turn with an hour gone, however, as the hosts appealed for a penalty after Olsson appeared to bring down Hazard in the area, only for the referee to wave the claims away.
Oscar went closest to putting his side further ahead with around 15 minutes remaining as he was denied twice in quick succession by Foster.
With the home side proving unable to further capitalise on their dominance, the Baggies started to threaten with ten minutes left on the clock as Cech was tested twice in a matter of minutes.
Substitute Peter Odemwingie forced the 30-year-old to tip over from a free kick before he then had to palm away a goalbound Azpilicueta header, but Cech and Chelsea held out for the three points.