McAuley was dismissed for a deliberate handball, conceding the penalty from which Rowlands netted his fifth goal of the season.
Leicester went ahead when Danny Tiatto's seventh-minute free-kick confused the Rangers defence and Patrick Kisnorbo nipped in front of Damion Stewart to head home.
It was the fourth consecutive match in which Rangers have conceded a goal inside the opening seven minutes.
It came after Dexter Blackstock had come within inches of putting the home side ahead when he steered Lee Cook's cross just wide.
And following Kisnorbo's opener, Blackstock squandered another opportunity. This time the former Southampton striker contrived to put the ball over from six yards after Leicester had failed to clear Rowlands' cross.
Another golden chance to equalise went begging when Cook's free-kick ran to Stewart, whose weak close-range shot was palmed away by Foxes keeper Conrad Logan.
At the other end, Simon Royce produced good saves to prevent Ian Hume and Elvis Hammond extending Leicester's lead before the break.
Royce, restored to the R's line-up in place of the dropped Paul Jones, pushed away Hume's shot at his near post and then did well to keep out Hammond 's 20-yard effort.
Rangers made a determined start to the second half and went close to levelling when Rowlands' right-foot volley from the edge of the area struck the post.
QPR got the equaliser they deserved on 69 minutes. Logan fumbled Rowlands' corner towards Blackstock, whose header was handled on the line by McAuley.
A penalty was awarded, McAuley was sent off and Rowlands calmly side-footed home from the spot.
Logan atoned for his mistake by keeping out Blackstock's header from Cook's lofted free-kick, before Blackstock fired wide after dribbling past Darren Kenton.
Defender Zesh Rehman missed a late chance to put Rangers ahead when he headed over following another expertly taken free-kick from the impressive Cook.
And Leicester substitute Matt Fryatt missed an even better chance with three minutes remaining.
Royce parried Hume's long-range shot straight to the unmarked forward, but Fryatt succeeded only in steering the ball back into the Rangers shot-stopper's arms.