The French coach believes that his team did well to recover from their Champions League exertions in Germany and gave everything in order to win.
"It was a difficult game away to Bayern [Munich] in midweek," Wenger told BBC Sport.
"The spirit we showed today was fantastic. We're up for the battle.
"We are in a battle which is where we want to be - we want to win games. We won today because we gave everything to win."
Victory sees Arsenal close the gap on fourth-placed Chelsea to two points in the Premier League table.