The Gunners made two alterations to the side which drew 2-2 with Crystal Palace, with Granit Xhaka and Nicolas Pepe being replaced by Lucas Torreira and Mesut Ozil – making only his second Premier League start of the season.
The visitors named an unchanged XI from the side which drew 1-1 at Newcastle United last weekend and they made the brighter start at the Emirates Stadium.
Ten minutes in home keeper Bernd Leno had to deal with a 25-yard free-kick from Joao Moutinho, with Wolves dominating much of the possession.
Ruben Neves smacked a long-range effort just over the crossbar as the visitors continued to impress, but they were hit by a sucker punch with just over 20 minutes played.
Alexandre Lacazette did the set-up work to give fellow striker Pierre-Emerick Aubameyang an easy chance to net his 50th goal for the club on only his 78th appearance for the Gunners.
Visiting keeper Rui Patricio then made a decent save to deny Torreira and keep the deficit at just a single goal, before repeating the trick to keep out a Lacazette drive.
Right on half-time Leno was in the right place to block a Matt Doherty strike and ensure his side went in at the interval a goal to the good.
The Germany goalkeeper was back in action early on in the second half as he made a fine save from Neves, who again tried his luck from the edge of the area.
On the hour mark Lacazette was withdrawn to be replaced by Gabriel Martinelli, while Wolves were forced to replace Doherty due to injury.
And the visitors eventually found an equaliser with 14 minutes left to play as Moutinho was allowed too much space and his cross into the area was met by Jimenez, whose header gave Leno no chance.