Seven days ago, the Gunners scored two own goals on the way to losing to Blackburn before having to come from behind to beat League Two Shrewsbury in the Carling Cup.
The Gunners looked as if they were destined for another troubling afternoon on Saturday 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 to see off the Lancashire side, although they were helped by David Wheater's sending-off 10 minutes into the second half.
Van Persie was at the forefront of Arsenal's excellent second-half display, breaking the deadlock with a low drive past Jussi Jaaskelainen in the 46th minute 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, a player who has had a bad-boy image in the past, took over from Cesc Fabregas as captain this summer and Wenger has been pleased with the Dutchman's leadership.
"Robin is a man who speaks his mind," Wenger said.
"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."
Wenger's team could have ended the day at the bottom of the Premier League table on Saturday 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 previous victory - against newly-promoted Swansea.
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 Saturday's 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 even if Szczesny made a good save at the start.
"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."
Wenger's joy was tempered by a knee injury to Walcott. The England winger limped off in injury time after pulling up on the halfway line with no-one around him.
Walcott is now a doubt for Wednesday's Champions League clash against Olympiacos and next Sunday's north London derby at Tottenham.
"I don't really know what happened with Theo," Wenger said.
"I thought it was a classic hamstring injury but it is not.
"He felt a sharp pain in his knee. I don't know what the diagnosis will be but it was completely surprising. I don't know if he will have scan tonight. I will have to speak to the medical staff."
Coyle, who has presided over five straight defeats now, said he would have to see a replay of Wheater's dismissal before judging whether Clattenburg made the correct call, but admitted the decision made a big impact on the game.
"Whether there was real contact, I don't know. I will need to see it back with David," Coyle said.
"I think it certainly made it more difficult. At half time we felt we had the platform to achieve a positive result but if you are going to shoot yourself in the foot as we did with 43 seconds gone in the second half it's obviously going to be difficult."
Source: Team Talk
Source: Team Talk