It was not for a lack of trying – Getafe goalkeeper David Soria pulling off a string of impressive stops, while Luis Suarez hit the woodwork.
Allan Nyom saw red for the hosts with 20 minutes left, yet Atleti could not make their numerical advantage count as they were forced to settle for just one point.
Perhaps spurred on by Real Madrid's earlier win, Atleti started with real intent – Suarez popping a header over before Soria denied Yannick Carrasco.
A rare error from Jan Oblak almost proved costly before the break, though Nemanja Maksimovic was unable to capitalise.
Oblak was back at his best on the hour, standing firm to deny Enes Unal after a sweeping Getafe counter.
Atleti were handed a boost with Nyom having his booking for a stamp on Renan Lodi upgraded to a red after a VAR check.
Getafe felt equally as hard done by from their next attack, the referee dismissing what seemed valid appeals for a penalty following Moussa Dembele's challenge on Maksimovic.
Dembele was in the thick of it at the other end soon after, twice testing Soria from close range – the first effort drawing a truly sensational stop – either side of Joao Felix forcing Getafe's goalkeeper into action.
Suarez thought he had won it in the closing stages, only for the post to come to Getafe's rescue, with a 90th-minute miss from Dembele ensuring Real Madrid and Barcelona were handed a boost.