Gervinho gave Arsenal an eighth-minute lead after he rounded Wolves keeper Wayne Hennessey following a superb through-ball from Israeli playmaker Yossi Benayoun.
But Wolves, now two points above the Barclays Premier League relegation zone, were level shortly before half-time after a corner fell to Stephen Hunt, whose shot took a deflection before Steven Fletcher reacted quickly to head in an equaliser.
Arsenal had a penalty appeal for handball by Christophe Berra turned down in a niggly second half, and Wolves were reduced to 10 men when Nenad Milijas was sent off by referee Stuart Atwell for diving in on Mikel Arteta.
Arsenal manager Arsene Wenger said his side had only themselves to blame for dropping two points at home.
"A second goal would have killed the game off," Wenger said on Sky Sports News.
"But I believe it was a question of us not making a mistake until half-time, and not to let them back in the game if they have something to hang on to.
"If they had to come out a bit more, it would have been a different story. That is where we still lack a bit of maturity, because look at how we lost the ball just before the corner.
"And how we played them on, I think we can only blame ourselves because we have not done well on that."
Wolves manager Mick McCarthy, meanwhile, vowed to appeal against Milijas's red card.
McCarthy described the decision as "harsh".
"I think there will be no doubt about it when everyone sees it, and I hope that when the referee sees it, he's magnanimous enough to know that he's made a mistake and he'll rescind it," McCarthy said on Sky Sports News.
The decision to send off Milijas perplexed McCarthy, who said: "It's just never a red card, that's why I walked across and shook his hand.
"I wasn't shaking his hand to annoy anybody.
"He's got his feet on the ground and he actually makes contact with the ball.
"I was so surprised that he sent him off but it just makes the performance even better, I think."
Jamie Mackie scored for the second match in a row as QPR rescued a point against fellow-promoted side Swansea.
Scotland winger Mackie struck shortly before the hour mark after latching on to a misplaced defensive header from Swansea's Leon Britton and firing home.