It was Everton who started the stronger and Tim Cahill so nearly opened the scoring after four minutes with an effort from inside the box, but it drifted just high of the post.
Buzsaky brought the best out of Howard with a free kick after 20 minutes, before Everton so nearly took the lead with an effort from Johnny Heitinga inside the area.
Everton took the lead after 31 minutes with a stunning effort from Royston Drenthe from all of 30 yards. QPR brought the game level after 36 minutes, however, when Bobby Zamora headed a Buzsaky cross into the net.
The home side missed a golden chance to take the lead moments before the break, when Buzsaky could only hit the post when it looked easier to score.
QPR continued to dominate proceedings in the second period with Adel Taarabt twice going close after 65 minutes, but the Moroccan could not find the target.
Shaun Derry was next to go close for the home side after 70 minutes, but his effort was thwarted by Heitinga.
Chances were few and far between in the latter stages, with both sides seemingly accepting a share of the spoils.
QPR will look to secure all three points when they travel to Bolton Wanderers next weekend, while Everton host Tottenham Hotspur.