After early goals Carlos García and Anthony Lozano inside the first 14 minutes for the home side, United fought back through an Anthony Martial penalty in the 21st minute and a Kobbie Mainoo goal three minutes after he came on as a half-time substitute.
But Cádiz would have the last word, with Rubén Sobrino converting a cross in the 57th minute and Tomás Alarcón adding a fourth in the 77th minute to give the side currently 19th in LaLiga the win.
The game was set up to keep players not involved in the ongoing 2022 World Cup in Qatar sharp ahead of the return of club football immediately following the winter tournament.
Man United's starting lineup included seven players that have featured in the Premier League so far this season -- Victor Lindelof, Aaron Wan-Bissaka, Scott McTominay, Donny van de Beek, Alejandro Garnacho, Anthony Elanga and Martial.
After quickly falling two goals behind, United started their comeback when 19-year-old midfielder Zidane Iqbal was fouled in the box and Martial scored from the penalty spot with a Panenka.
Mainoo, a 17-year-old midfielder yet to make his competitive first-team debut, then drew the visitors level with a deflected effort from just inside the box.
Both sides made wholesale changes at half-time with United substituting all 10 outfield players and Cadiz making nine alterations. It was the hosts that adapted the better, going on to score the victory.
Erik ten Hag's side will also take on Real Betis in Spain on Saturday before competitive games return following the World Cup with a Carabao Cup round of 16 matchup at home to Burnley on Dec. 21 -- three days after the World Cup final.