Football: Century for van Persie as Arsenal down Bolton
Van Persie put his side ahead in the 46th minute with his 99th strike for the club before netting his 100th goal midway through the second half.
By then Bolton's David Wheater had been sent off for a foul on Theo Walcott, ending the visitors' hopes of staging a recovery and ensuring Wenger's side claimed only their second league win of the season while condemning Wanderers to a fifth successive defeat.
Alex Song wrapped up the win in the 89th minute and the victory strengthened Wenger's claim before this game that his side had the mental strength to haul themselves out of a difficult period.
Wenger had also reaffirmed his intention to protect his young players from criticism with a somewhat bizarre claim that it was his job to "absorb the bullets, like a polar bear."
There has certainly been plenty of criticism directed the way of Wenger and his players during a woeful start to the season with the manager placed in the uncomfortable position of being forced to defend his record at the club.
And the news that midfielder Jack Wilshere would now be out at least until December after undergoing ankle surgery did nothing to lift spirits at the Emirates Stadium.
Bolton manager Owen Coyle also sprang a surprise by opting to leave Kevin Davies on the bench despite the striker's record of causing Arenal problems over the years.
In Davies' place, David Ngog was handed responsibility to lead the visitors' attack and the Frenchman made an immediate impact, forcing Arsenal keeper Wojciech Szczesny into a good save in the second minute.
The chance had come about because of the home defence's failure to deal with a high ball into the box - too often a weakness this season.
Wenger's side responded quickly with Gervinho sprinting clear five minutes later only to overrun the ball, allowing Jussi Jaaskelainen to race off his line and smother the danger.
That incident summed up much of Arsenal's forward play during the first half with Wenger's side lacking conviction in the final third.
Van Persie fired narrowly wide with a well-taken free kick but Jaaskelainen was barely troubled before the break.
Fortunately for the home side, Bolton were similarly lacking in confidence and the introduction of Davies after 20 minutes following an injury to Ngog made little difference to the pattern of play.
Had the stalemate persisted after the break, Wanderers would have felt confident of claiming at least a point, but they allowed Arsenal to forge ahead immediately after the restart and from that moment their chances disappeared.
Coyle's side were guilty of conceding possession near the halfway line allowing Aaron Ramsey to surge forward and release Van Persie whose low shot beat Jaaskelainen at the near post.
Wheater then made his own contribution to Bolton's downfall, foolishly holding Theo Walcott back on the edge of the box when the winger was set to burst clear on goal to earn a red card.
Undermanned, Bolton at least managed to create their best chance of the second half when they broke through Chris Eagles whose tame shot was saved.
Van Persie then doubled the lead in the 71st minute when he produced a neat flick to turn home Walcott's low cross and Song made it three in the final moments with an 18-yard effort.
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