It made little difference as they outplayed Palace in the second half with Kortney Hause heading in from close range to double their lead in the 66th minute.
Villa climbed to sixth in the standings with 25 points from 13 games while Palace stay in 13th place.
Striker Watkins did not manage to increase his season's Premier League tally from six but the 24-year-old was instrumental in Villa's win with assists for each goal.
"A massive win, it's always hard going a man down. You have to press at the right times and be structured as a team and I feel like we did that," man-of-the-match Watkins said.
The clash was the first Boxing Day game ever shown live by the BBC and it did not take long to provide entertainment.
Watkins's angled shot was parried by Palace keeper Vicente Guaita in the fifth minute, the ball falling for Traore who picked his spot to give Dean Smith's side the lead.
Zaha and Mings tussled throughout the half and were booked for a scuffle and then on the stroke of halftime Zaha wrong-footed Mings who dragged him down and referee Anthony Taylor had little choice but to send the England defender off.
Palace made little headway in the second half though and Villa doubled their lead when Watkins headed against the crossbar and Hause was alert to nod in the rebound.
Villa revelled in the open spaces allowed as Palace pushed forward trying to find a lifeline and from one counter-attack, Jack Grealish found Watkins who then set up El Ghazi to smash a shot into the net via the woodwork.