A move from a corner then saw Clint Hill play in Benayoun, and the midfielder slotted the ball in from the centre of the box.
Wigan responded well to going behind, but James Perch was unable to beat Green with a well-struck shot. The QPR goalkeeper also had to be alert to tip away James McClean's low effort.
Despite being ahead, QPR struggled to contain the Latics, who were the stronger side as the match reached half time.
The hosts needed Green to pull off a decent stop from James McArthur's shot just after the restart, but the crossbar came to their rescue moments later as Ivan Ramis's header beat Gary O'Neil on the post.
With the game opening up, Tom Carroll fired straight at Ali Al-Habsi from the edge of the area, while Morrison smashed a free kick against the crossbar.
Benayoun was sent off late on for a second bookable offence, but the home side held on for the win.