The Scottish international was bundled over in the penalty box after 86 minutes by United defender Michael Duberry - a summer transfer target for Wolverhampton.
Referee Keith Lowe immediately gave Duberry his marching orders for the clumsy challenge and awarded Wolves a spot-kick.
Miller, who made no mistake with his penalty against Stoke a weak ago, fired in a low, hard shot, only for goalkeeper Neil Sullivan to dive and push the ball away.
The miss cost Miller the opportunity to make it three goals in three games and left Wolves with just two points in the bank from the fist three games of the campaign.
Leeds, with just one win to their credit since they were relegated, created little to trouble the home defence, with Danny Pugh firing in their only on-target effort of the opening 45 minutes - a 20-yarder that was held comfortably by Paul Jones.
It was always Wolves who were in control, with teenage striker Leon Clarke keeping the Leeds defence on their toes.
The youngster powered an eighth minute header just over the crossbar and moments later he had a good shot well saved by Sullivan.
After the break, Sullivan had to react sharply to keep out another low shot from Clarke, while Miller fired in an effort that flew just inches over the crossbar.
Frazer Richardson, Michael Ricketts and Simon Walton all got shots in for Leeds, but they all flew high or wide of the Wolves goal.
Leeds boss Kevin Blackwell made changes to his line up after their disappointing midweek defeat at Gillingham, but once again the Whites failed to click into gear when a better display might have gained maximum reward.