A Bamba Anderson own goal after only two minutes helped the Wolves on their way to victory, although Alexander Meier levelled before the break.
Arnold, decisive in Wolfsburg's previous two wins, then clinched victory in the 82nd minute as Dieter Hecking's men made it three wins on the spin to rise above Schalke in the standings.
Wolfsburg got off to a flyer thanks to Anderson, who turned Patrick Ochs' cross into his own goal as he beat Ivica Olic to the ball.
The visitors looked to build on their lead and Ivan Perisic nearly did that when he burst through but dragged his shot just wide of the far post.
Frankfurt slowly but surely started to find a route back into the game and it was no surprise that it came from Meier, who has not scored more goals against any other side than Wolfsburg.
He curled a direct free-kick over the wall, with Diego Benaglio unable to reach the side of the goal he thought he had covered, and the hosts were back on terms 10 minutes before the interval.
Meier was Frankfurt's biggest threat throughout and his volley in the 74th minute was the closest they came to taking the lead.
Instead, it was Arnold who stole the headlines for the third week running with the winner in the 82nd minute.
Ochs was the provider again with another vicious ball from the right and Arnold, who was played onside by Zambrano, just had to stick out a foot to guide the ball past Kevin Trapp and earn the Wolves all three points.