The strugglers came into the game two points from safety at the bottom of the table, but lifted themselves to 17th with just their fifth win of the season.
Suarez's goal arrived in the 21st minute and would have graced any stage.
After Rayo partially cleared a free-kick, the ball ran loose to the defender, who smashed an effort into the top right-hand corner from 30 yards.
Rayo then saw Raul Baena dismissed 14 minutes from time after picking up a second caution and six minutes later, substitute Garry Rodrigues exchanged passes with Faycal Fajr and slotted low into the net to seal all three points.
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