Both Mario Suarez and Diego Godin were dismissed for the third-placed visitors who now trail city rivals Real Madrid by three points in La Liga.
Atletico had the better of what few chances were created but star striker Radamel Falcao had a rare off night.
The Colombian could have opened the scoring in the sixth minute but could only push a tame effort wide from six yards after running on to Diego Costa's left-wing centre.
Falcao at least hit the target six minutes before half-time but his header was straight at Getafe goalkeeper Jordi Codina.
In between, Getafe offered little threat with a 20-yard shot from Angel Latifa straight at Thibaut Courtois the best they could muster.
The second half started slowly but flickered into life after 68 minutes when Godin was adjudged to have tripped Adrian Colunga. Television replays showed the offence - for which Godin received a yellow card - had taken place a yard inside the penalty area but referee Ferreiro Delgado gave only a free-kick on the edge.
Abdelaziz Barrada took the free-kick but his curling effort flashed inches wide with Courtois beaten.
Suarez was the first Rojiblanco to see red four minutes later, picking up his second caution for a needless handball near the halfway line.
The 10 men still looked dangerous going forward and substitute Cristian Rodriguez's surging run from the halfway line was not matched by the finish as he blasted his effort over.
Courtois did well to keep out a Fernandez Borja drive after 83 minutes before Atletico were reduced to nine in injury-time as Godin was shown a second yellow card for an elbow on Alvaro Vazquez.