Eze calmly netted from the spot after Bright Osayi-Samuel was fouled by Martyn Waghorn, who had put Derby ahead.
The 21-year-old has now scored seven goals in 19 league appearances for QPR this season.
Rangers are now without a win in their past seven matches and are still yet to keep a clean sheet this season.
But they battled back well after falling behind midway through the first half and more than deserved a draw.
After Luke Amos’ careless foul on Jack Marriott near the edge of the penalty area, Waghorn found the top corner of the net with the resulting free-kick.
Rangers responded strongly and Derby keeper Ben Hamer pushed away shots from Ryan Manning and Jordan Hugill before the equalizer.
