The home side fought back admirably and was in fact unlucky not to take all three points in a turgid affair at Loftus Road.
Royston Drenthe's long-range strike on the half-hour mark was as much as Everton deserved following a dominant start to proceedings. However, once Zamora drilled his header past Tim Howard five minutes later, Mark Hughes' men made all the running.
Zamora's equalizer was his second goal for his new club and the relief felt amongst the fans was justified given their recent southerly slide towards the relegation zone.
It was Everton which took just three minutes to fashion the first chance of the game. Tim Cahill was first to a loose ball in the box following a free kick from wide but his left-footed volley struck the middle of Paddy Kenny's crossbar.
Though the away side controlled possession better in the opening stages, QPR highlighted its threat through a volley of its own. Akos Buzsaky's well-struck but misguided shot from outside the box was helped on by Shaun Derry but his deft touch saw the ball just drift wide.
Set pieces took on an expected prominence and with Buzsaky delivering teasing crosses from wide, it was any wonder QPR didn't open the scoring. Clint Hill was most guilty, heading over the crossbar when it seemed easier to score.
Buzsaky continued his encouraging start following his recall to the midfield and his low free kick from 20 yards required a good first save from Tim Howard.
Both sides traded set-piece chances and Drenthe's deep cross from the right flank was flicked on by Sylvain Distin into the path of John Heitinga. The Dutch defender failed to get a firm touch and his nudge at goal was gathered by Kenny on his line.
QPR's left flank summed up the good and the bad from its first-half performance. While Armand Traore was menaced by Drenthe's trickery, Adel Taarabt found space to cross for the arriving Shaun Wright-Phillips. The diving header was well met but just zipped by Howard's left-hand post.
Then, on the half hour, came the opening goal. Marouane Fellaini robbed QPR of possession in midfield and Steven Pienaar collected the ball and shifted it inside to Drenthe.
In the middle of the pitch and 30 yards out, the Dutch winger traveled forward, jinked onto his left foot and smashed a low drive into Kenny's bottom corner.
But QPR still offered a danger to David Moyes' side and as Drenthe was booked for a poor tackle on Taarabt on the byline, Buzsaky trotted over and sent yet another teasing delivery into the six-yard box.
Zamora made the cross his own, finding the space to guide a powerful header beyond Howard and level the game.
The goal came to the relief of thousands of Rangers fans but their side was not to sit on its laurels.
In a frenzy of goalmouth action QPR managed to hit both posts and failed to score. First, Taarabt ran onto a cutback on the left corner of the box and curled his effort past Howard and onto the far post.
The rebound ensured the chance was still alive though and as Zamora squared his pass to Buzsaky, everyone in attendance was convinced the second home goal would arrive. To great surprise, though, Buzsaky inexplicably contrived to guide his tap-in off the foot of the other post.
The moment of slapstick finishing proved to be costly though, as Rangers failed to conjure a chance as clear cut again.
Though the break came at a bad time for Hughes' outfit, QPR continued to look the better side after the break and Derry's back-post volley whistled wide of Howard's post.
Taarabt, who was having one of his better days, showed pace and intent to glide down the left and into the box. His left-footed shot across Howard was well hit but lacked accuracy.
David Moyes reacted by throwing on Nikica Jelavic and Leon Osman for Cahill and the impressive Drenthe. But as the Toffee's shape moved to a 4-4-2, QPR began to find more holes.
The game was finely poised and with 20 minutes remaining. There was a sense that the next goal would be the winner and although Jelavic buried a shot past Kenny from an offside position, there wasn't a genuinely clear goalscoring chance created in the final stages.
Taarabt's withdrawal seemed a bizarre move from Hughes, given the Moroccan was the home side's creative fulcrum and indeed, his substitution marked the conclusion to the threat of QPR's play.
With Everton happy to return to Merseyside with a point, Kevin Friend was left to blow for fulltime and end a dogged encounter 1-1.