A first-half double from Chile forward Alexis Sanchez was enough to move the Gunners ahead of Manchester City into third and four points clear of fifth-placed Manchester United.
The match was played out in front of a smaller than usual crowd at Emirates Stadium. The club confirmed that 59, 568 tickets had been sold although thousands of empty seats were visible in the 60,432-capacity arena.
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“You look at the table and you know that for us every point is important at the moment,” said Wenger. “We are under permanent pressure for everything again so it is important to have the lead early and focus on the way we want to play football.
“We want to finish as high as possible. You never know what will happen in front of you, there can still be twists and turns. We want to win our games.
“I don’t know where we finish but we have to give absolutely everything in every game.”
Despite a campaign which has once again seen a promising Arsenal title challenge wilt – this was just their sixth victory in 15 league matches – Wenger urged the supporters who opted to stay away to return.
“My message is to come and support the team,” added Wenger. “If you love football, you go out there and I think you will see quality football. That’s what we try to give to our people.”
Arsenal seized control of the clash in the sixth minute as Sanchez shimmied past Sandro and thumped a low shot past Baggies goalkeeper Ben Foster.
The hosts doubled their advantage seven minutes before the break as Sanchez notched his second of the night, and fifth in four games, with a clever free-kick.
With a packed wall to his right and the assistance of Per Mertesacker and Olivier Giroud who peeled away from the blockade, Sanchez scooped the ball into the left hand hand corner of the goal before Foster could respond.
West Brom’s best chance of snatching something came from set pieces; Gareth McAuley hit the bar with a header from a corner after half an hour and with twenty minutes to go Salomon Rondon failed to connect with another despite a gaping goal.
These were rare forays forward as the visitors were primarily occupied with stemming the flow of Arsenal attacks that almost resulted in a third goal as Aaron Ramsey, Alex Iwobi, Mesut Ozil, Giroud and Joel Campbell all spurned chances.