Wolves broke the deadlock in the 57th minute when left-back Stephen Ward saw his low cross-shot deflected into his own net at the near post by Lee Peltier.
But their advantage was short-lived - lasting just seven minutes - as Luke Varney latched on to a pass from Ross McCormack and curled his right-foot shot beyond goalkeeper Carl Ikeme.
McCormack then made no mistake from the spot in the 77th minute after Bakary Sako was adjudged by the assistant referee to have fouled Sam Byram.
But Danny Batth's first league goal for Wolves, heading home Jamie O'Hara's cross, denied Leeds the win that would have boosted their top-six hopes.
He said: "The frustration for me is that we have just played Cardiff City and Wolves and we should have had six points and I've got one out of both games.
"I want to get into the play-offs and I am disappointed that we are not in the play-offs and games are running out.
"I want to go up. I think I am more frustrated than anybody. It is all right for the players they are all young and they can play for years to come.
"I want to get into the play-offs so I am frustrated over the last two games. But I am ever so pleased the way we have played since the Barnsley debacle. It is good for the future.
"At least I have the team that I want together at the moment. I can't fault anyone now. This is the team that I would like in the trenches with me if we were going to war. You know what I am like. Everyone is genuine. A manager asks for them to give their all and they did. But the games are running out."