Benzema played one-twos with Toni Kroos and Marco Asensio before curling a low show into the bottom corner from outside the penalty area.
Benzema went close to adding another from long range but Real's second goal eventually came from the penalty spot.
Lucas Vazquez took a poor first touch but still managed to draw a foul out of Salvador Reyes.
Hazard stepped up and scored with a precise drive, even though keeper Oscar Jimenez dived the right way.