Aleksandar Mitrovic bagged a hat-trick as the Cottagers moved four points clear of the Baggies for second place in the EFL Championship table.
Story of the match
On the quarter of an hour mark, Kebano had a sight of goal with a looping volley that was just narrowly wide.
Kebano then set up Jean Michael Seri, who fired over and at the other end, a header by Semi Ajayi teed up Phillips, who blasted over.
Perhaps the visitors' best chance of the first half came when Matt Clarke got on the end of a deep free-kick, a superb save from Fulham goalkeeper Marek Rodak preventing the match from being even.
In the 40th minute, the hosts doubled their advantage as Seri won the ball from Robert Snodgrass and it squirmed to Mitrovic, who poked home.
Early in the second half, Conor Townsend had a sight of goal down left-hand side, but he went just wide.
Clarke accidentally squared a quick free-kick into the path of Kebano, but he didn't find the finish needed to beat Johnstone.
With 20 minutes left, the Baggies were reduced to ten men when Darnell Furlong took down Wilson and was subsequently dismissed.
Kebano and Bobby Decordova-Reid had chances with the man advantage, but neither could finish. Tosin then shot straight at Johnstone.
Late on, Fulham would get their third as Decordova-Reid curled a pass to Wilson, who squared for Mitrovic to finish and complete his hat-trick, his second of the season.
Tosin was sent off with five minutes to play, but the game was well in hand as the Cottagers look to be in strong position for promotion.
Man of the match: Aleksandar Mitrovic
Who else would it be? While he received terrific service, with the play of Kebano standing out, the Serb showed why he's one of the most feared strikers in English football and looks set to carry Fulham back to the top-flight.