A goal in each half took Olivier Giroud's season tally to 10 and stretched Arsenal's advantage at the Premier League summit to four points as they bounced back from defeat to Manchester United before the international break.
Match-winner Giroud was given a considerable helping hand midway through the first half when he capitalised on a horrible error of judgement from Southampton goalkeeper Artur Boruc.
Mauricio Pochettino's men demonstrated the poise and ambition that has seen them take points off Liverpool and Manchester United on their travels this term thereafter and Giroud's late penalty did nothing to temper Wenger's admiration.
"I'm very happy because we were against a good team and they showed why they made good results before," he told BBC Sport.
"We couldn't take our chances but we took advantage of their mistakes. It's a very good win against a difficult team. They stopped us well from playing.
"It (Boruc's error) happens. Players are quick to close down. Maybe he was a bit too confident and Olivier Giroud did very well.
"When you see Southampton play today we know why they won at Liverpool and drew against Manchester United. They are a good team and if they had won today they would have been level with us at the top of the league, so that shows you how good they are."
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