Zinedine Zidane's squad won the penalty shootout 4-1 on kicks by Carvajal, Rodrygo, Modric and Sergio Ramos after the clubs played a 0-0 draw in regulation time and overtime on Sunday evening, reports Efe news.
Atletico's Saul, who hit the post, and Thomas, whose shot was stopped by Thibaut Courtois, missed while Trippier scored the club's lone point in the shootout.
Real Madrid has now won 11 Super Cups, having previously claimed the title in 1988, 1989, 1990, 1993, 1997, 2001, 2003, 2008, 2012, and 2017.
Real Madrid's Fede Valverde was voted the Man of the Match but was unable to finish after getting a straight red card for a tactical foul that prevented Atletico from scoring a goal.
The 21-year-old Uruguayan midfielder was tossed out from the match with five minutes of regulation time remaining for preventing Atletico's Alvaro Morata from scoring what appeared to be a sure goal by taking him down from behind.
Valverde will miss Real Madrid's La Liga match against Sevilla because of his ejection from Sunday's match.
The two clubs were unable to score on the few opportunities they had in regulation time.
Real Madrid went into overtime short of a man due to Valverde's ejection in the 115th minute, but managed to pull off the win, thanks to its performance in the penalty shootout at King Abdullah Sports City.
Zidane, an expert on winning finals and titles, has now won two Super Cups with the club.
( With inputs from IANS )