Van Persie was at the forefront of Arsenal's second-half display, breaking the deadlock with a low drive past Jussi Jaaskelainen before adding his second by turning home Theo Walcott's cross with a clever flick. The brace took the Dutchman to 100 goals for the London club - a credible achievement given he has started just 175 games since moving from Feyenoord seven years ago.
Van Persie took over from Cesc Fabregas as captain this summer and Wenger said: "Robin is a man who speaks his mind. I think he is one of these guys who develops with responsibilities. You would think he is not a natural captain at the start but he really has grown well into the role. I have observed him and he does well there."
Seven days ago the Gunners scored two own goals on the way to losing to Blackburn. The Gunners looked as if they were destined for another troubling afternoon when they started poorly against Owen Coyle's team, particularly when Wojciech Szczesny had to pull off a brilliant save to deny Bolton's Darren Pratley in the third minute.
But the London club put in a sublime second-half performance, although they were helped by David Wheater's sending off 10 minutes into the second half.
Wenger's team could have ended the day at the bottom of the Barclays Premier League table if they had lost and West Brom and Fulham had drawn. The Gunners had been left in the precarious position by a poor start which had seen them complete just one victory.
Arsenal chief executive Ivan Gazidis felt it necessary to give Wenger his public backing this week after some fans had called for a change in manager. Wenger thinks the criticism aimed at him and his side was slightly unfair following the Blackburn game but was nonetheless a relieved man after this victory.
"It was a good win for us because we cannot drop points anymore," Wenger said. "We will not lose every game like we did at Blackburn. We had 22 shots on goal there and in the end we lost.
"Today it was a question of nerves, patience and intelligence. I think we controlled the whole game. But in the second half I could not see Bolton scoring a goal. And when they were down to 10 men it made it even more difficult for them."
Source: PA
Source: PA