ALEXIS Sanchez denied Albion their final chance of completing a double this season with two well-taken first-half goals.
The Baggies were never able to recover from falling behind after just a few minutes and then conceding a second just before the break.
It took just six minutes for the hosts to go ahead. Laurent Koscielny played the ball to Alexis, who twisted past Sandro, some 30 yards from goal, and drove low shot to Ben Foster's right - a strike the Albion goalkeeper had little chance of keeping out.
Albion had made one change to their previous starting line-up with Sandro replacing Salomon Rondon, but it was Arsenal who continued to show most enterprise early on.
And yet Albion could have been level on 28 minutes. The visitors' third corner of the game was their finest so far - James McClean planted his flag-kick onto Gareth McAuley's head, with the ball flying past Petr Cech and onto the crossbar.
At the other end, Arsenal were close to making it two. Lovely play by Aaron Ramsey and Hector Bellerin unlocked Albion's left-hand side, with the cross field pass finding its way to Mesut Ozil, whose shot went through the legs of Alexis and Foster, nicking a touch against the Albion goalkeeper's leg. Craig Dawson cleared as the ball trickled towards the goal.
Alexis doubled Arsenal's lead in the 38th minute. Claudio Yacob brought down Ramsey on the edge of the box, with Alexis curling a brilliant free-kick between McClean and James Chester to beat Foster.
Albion were to go close in their opening attack of the second half when McClean rose to meet Dawson's excellent right-wing cross, but his strong header didn't get the better of Cech.
ARSENAL: Cech, Bellerin, Koscielny, Mertesacker, Monreal, Ozil (Walcott 85), Ramsey, Elneny, Iwobi (Coquelin 82), Giroud, Alexis (Campbell 85)
Subs: Ospina, Gabriel, Chambers, Welbeck.
ALBION: Foster; Dawson, McAuley, Evans, Chester (Olsson HT); Sessegnon, Fletcher, Yacob, Sandro (Rondon HT), McClean (Gardner 65); Berahino.
Subs: Myhill, Anichebe, Leko, McManaman.
Bookings: McAuley (41, foul)
Referee: Jon Moss (County Durham)