كتب : Ahmad Saied
Abdoulaye Diagne-Faye opened the score line in the ninth minute and Anelka widened the gap in the 45th minute.
But Arsenal skipper Gilberto Silva pulled one back just before the half-time whistle before Frenchman Anelka wrapped up the victory at the Reebok Stadium in the 76th minute.
The visitors were unlucky as Freddie Ljungberg, Emmanuel Adebayor and Cesc Fabregas rattled the woodwork in the second period.
Tempers flared on the pitch as players from both sides got aggressive, forcing referee Mike Dean to hand up seven yellow cards.
Arsenal's third defeat of the season left them in sixth place with 22 points, 12 adrift of leaders Manchester United, who will take on title holders and second-placed Chelsea on Sunday.
Bolton moved up to third spot on 24 points, one ahead of Portsmouth and Aston Villa, who lie fourth and fifth respectively.
Adebayor failed to break the deadlock after being fed by Fabregas and Theo Walcott, who made his first Premiership debut only for Diagne-Faye to punish the Gunners for squandering easy chances.
He cut ahead of marker Kolo Toure and Arsenal's static defenders to connect with El Hadji Diouf corner-kick, heading home despite a desperate attempt from goalkeeper Jens Lehmann.
Former Arsenal star Anelka scored his first Premiership goal since joining Bolton in the summer when he controlled a long pass on the left, cut inside and fired an unstoppable bullet from the edge of the area into the top left corner of the net.
In the same minute, Brazil's Gilberto, who captained Arsenal in the absence of injured Thierry Henry, narrowed the gap when he rushed inside the box to head a perfect cross from Fabregas into the back of the net.
Ljungberg almost leveled after the break but his header from Walcott's cross hit the left post and went wide.
Anelka put the last pin in Arsenal's coffin when he latched on to a long pass before dinking into the far angle past the advancing Lehmann.
Arsenal came close from scoring in the last three minutes when Fabregas' pass found Adebayor in the area but the lanky striker blasted the ball into the crossbar before Fabregas himself was denied by the post.