The away side rushed out of the blocks in the opening period and created a series of chances in the first five minutes.
Matt Phillips, who set up Austin's earlier chances, himself went close in the 12th minute when the right winger cut inside onto his left foot and rifled a low shot inches wide of the near post.
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Pavel Pogrebnyak then poked the ball wide in the 27th minute as the home side began to forge out some openings.
However, QPR continued to create openings as Austin tested McCarthy once more with a diving header before the goalkeeper was called into action again in the 41st minute to tip Hoilett's fierce, low drive around the post.
Fifteen minutes after the restart, McCleary scored the game's opening goal in fine fashion. The midfielder picked the ball up and skipped past Barton before firing a 25-yard shot off the post and into the back of the net.
Austin, who was a menace all afternoon, tested McCarthy once more in the 70th with a fiercely struck volley before Obita was denied by the outstretched foot of Green.
With 12 minutes remaining, Barton got his side back on level terms with a delicately-placed free kick from the edge of the box and celebrated by holding aloft a shirt bearing the name of Alejandro Faurlin, who has been ruled out for the rest of the season with a cruciate knee ligament injury.
The visitors almost stole all three points with five minutes remaining, but Andy Johnson's volley dropped just wide of McCarthy's far post.