Arsenal completely dominated the first half hour but the hosts fought back after an early tactical substitution by coach Henk ten Cate who brought on Dennis Rommedahl.
In a poor match, Van Persie gave Arsenal the win in the tournament when he hit the net from five metres following an impressive run by Gael Clichy.
Arsenal finished top with nine points, three for each win and one for each goal scored.
Atletico Madrid finished second with six points following a comfortable 3-1 win over Lazio, while Ajax were third with five points.
Braulio Rodriguez opened the scoring for Atletico from close range after 38 minutes, while Luis Garcia doubled the lead midway through the second half.
Stefano Mauri pulled one back for the Italians but Jose Antonio Reyes registered his first goal for Madrid two minutes later to settle the match.