The 28-year-old striker scored twice in the space of four minutes midway through the first half to put Arsenal in charge against Newcastle United.
Moussa Sissoko halved the deficit in the 48th minute, but despite late pressure from the home side, the Gunners managed to hold on for three points.
Arsenal manager Wenger, whose side crashed out of the Champions League on away goal at Monaco mid-week, challenged his players to keep their winning run going.
Wenger told BBC Sport: “We want to finish as high as we can, we have 60 points with eight games to go. If you look at the points we have taken in the last three months, it has been outstanding. So we just want to win and win and win.”
Arsenal are four points behind Premier League leaders Chelsea after Saturday’s 2-1 win, although Jose Mourinho’s side have played two games less than their London rivals.
The Gunners make the trip to Manchester United next weekend as Wenger’s men look to replicate their 2-1 victory over the Red Devils in the FA Cup quarter-final at Old Trafford earlier this month.
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