Zaragoza's Ivorian midfielder Ndri Romaric was shown a straight red card for a studs-up challenge after only nine minutes, and his team mate Alvaro Gonzalez followed him down the tunnel after conceding a penalty in the 63rd.
Getafe's Diego Castro netted from the spot, though Zaragoza keeper Roberto almost saved it, and the visitors themselves finished the game with 10 men when Abdelaziz Barrada also saw red for another studs-up challenge near the end.
Getafe climbed to seventh level on 10 points with champions Real Madrid, who are sixth and visit leaders Barcelona (18 points) on Sunday for the first league 'Clasico' of the season.
Earlier, Rayo Vallecano also moved on to 10 points from seven games in eighth place after living dangerously before winning 2-1 at home to promoted Deportivo La Coruna.
Piti put the hosts ahead at the far post in the 18th minute and former AEK Athens winger Jose Carlos, perhaps their best player on the day, fired in a deflected second goal soon after.
Depor pulled one back from the penalty spot before halftime and in the second period both sides put in an entertaining, if error-strewn, display which could have gone either way.
In other action, Oscar Gonzalez's header 10 minutes from time stopped 10-man Espanyol their first win of the season as Real Valladolid earned a 1-1 draw. Victor Alvarez was sent off after two yellow cards.
Espanyol had grabbed the lead on 70 minutes courtesy of Joan Verdu's penalty after Samuele Longo was deemed to have been pushed by Antonio Rukavina.
Real Betis completed a 2-0 win over Real Sociedad with Paulao (18) and Ruben Castro (80) on target. Mario of the home side was sent off in the dying seconds for aiming a kick at Xabi Prieto having been booked earlier.