Sanchez's strike was his 20th Premier League goal of the campaign, the first time he has reached that landmark since joining from Barcelona.
Arsenal moved above Manchester United into fifth on 66 points, three adrift of fourth-placed Manchester City with both having played 35 games.
"I know we can go forward and score goals".
They are now three points behind West Brom, who are in eighth place, and the Saints will be looking to win this match which is their game in hand on the teams above them. They were certainly not playing like a team that had to win the match to keep their faint top-four hopes alive. It's a tight hamstring. We haven't had any interest, in fairness, but we would look at things if the right offer came in'.
"We know we can only win our games and we had a strong performance on Sunday (beating Manchester United 2-0) and a strong performance today".
Wenger confirmed Hector Bellerin will replace Oxlade-Chamberlain if the England man is not fit to travel to Stoke and praised the Spain international's mentality after he was recently jeered by Gunners fans following a gutless defeat at Crystal Palace last month.
Sanchez had been quiet, but with 15 minutes on the clock in the second period he made the breakthrough.
Sanchez collected a pass from Mesut Ozil and sent two defenders sprawling to the ground before switching directions and slotting a composed left-footed finish past Fraser Forster.
After coming close to setting a Premier League record for assists in a single season last term, Ozil has enjoyed his best goalscoring form since moving to North London this season but his attitude has been critics.
"The goal he scored tonight shows what he's about: very good technique in a short space".
Arsenal are fifth in the standings and have an outside chance of finishing in the top four for the 21st consecutive season.
"It's often the same against the big six", said the Frenchman. "Every time it was interesting, I think, the play. We know it's our last chance, we know we need to win all our final games if we are to have any kind of positive achievements to take from this season". For them, in one situation, they scored.
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