Van Persie's 30-yard effort hit Stephen Clemence and left heroic goalkeeper Maik Taylor stranded. Taylor's brilliant saves had defied Arsenal for almost an hour, after Blues skipper Kenny Cunningham was sent off in the 24th minute for a professional foul on Freddie Ljungberg. The keeper even saved a Robert Pires penalty.
The defeat leaves Blues uncomfortably close to the relegation zone having won only six points from eight matches.
Steve Bruce's squad was ravaged by injuries, and suspensions for Nicky Butt and Neil Kilkenny. The Blues boss had only 14 fit senior players to choose from. Sixteen-year-old Sone Aluko was named among the substitutes after making just two reserve appearances.
Walter Pandiani and Emile Heskey started in attack in a 4-4-2 formation. Heskey later fought a lonely duel with Sol Campbell - in front of watching England coach Sven-Goran Eriksson, after Cunningham's dismissal.
Both teams survived early scares. Clemence made a second-minute challenge to stop Ljungberg as he prepared to shoot after a neat one-two with Jose Antonio eyes. A minute later, Ashley Cole cleared off the line from Heskey with Lehmann beaten after Pandiani's pass had played the striker through.
Arsenal struggled for fluency in midfield and too often they uncharacteristically gave the ball away. Aleksandr Hleb was a particular offender.
The game turned on Cunningham's 24th-minute dismissal. Gilberto's throughball freed Ljungberg and Cunningham, the last defender, brought him down and referee Chris Foy immediately showed him the red card.
Taylor then made a flying save from Reyes' swerving free-kick - the first of many. Two minutes later, Damien Johnson brought down Ljungberg inside the box and Foy pointed to the penalty spot. Taylor beat out Pires' weak kick and the Frenchman hit the rebound into the side-netting.
Reyes blasted over the bar, Taylor palmed away another Reyes strike and then dived low to thwart the Spaniard. Cesc Fabregas headed straight at the keeper as Blues somehow survived until the interval.
Fabregas opened the second half with a shot that flew inches wide, after Pires seized on Johnson's error.
Taylor denied Arsenal again, with a brilliant save from Ljungberg's blast after a lightning counter-attack led by Reyes. He pulled off an even better stop in the 54th minute, tipping Pires' shot onto a post after Fabregas had split the Blues defence.
However, Blues almost scored in a 59th-minute breakaway when Heskey, falling backwards, scooped Jermaine Pennant's pass at Lehmann.
Arsenal's anxiety grew. Bergkamp replaced Hleb after an hour and Ljungberg returned to the right flank. Taylor saved again from Reyes and Arsene Wenger sent on van Persie as Arsenal tried desperately to beat Taylor.
Jamie Clapham was lucky not to concede a spot kick after taking out Reyes while at the other end, Matthew Upson flashed a header over from a free-kick.
Then van Persie's 81st-minute effort broke the deadlock. He picked up a weak clearance and hit a low shot through a crowd of bodies. The ball struck Clemence and deceived Taylor who could not readjust in time.
Kolo Toure robbed Pennant in the dying minutes to preserve Arsenal's lead. Olivier Tebily headed the resulting corner past Lehmann but an assistant had signalled that the ball had already gone out of play. That seemed to sum up Blues' afternoon.