The former Fulham striker stooped low to head Park Ji-Sung's cross goalwards but his effort narrowly went wide of the post.
Rangers were ahead moments later when Shaun Wright-Phillips ended his two-year scoring drought with a low finish from Zamora's through pass.
From the resulting corner, Ashley Hemmings came within inches of finding an equaliser when his header struck the crossbar.
QPR then regained control of the game and put the match beyond doubt courtesy of more fine work from Zamora, who stayed cool to chip the keeper when put through one on one.
Bosingwa completed the scoring with a debut goal when he hooked in a close-range effort after Walsall keeper David Grof had parried Zamora's fierce shot.
The result is Rangers' first win of the season after they recorded a draw and a defeat in their opening two Premier League games.