The Uruguayan glanced in a lofted pass from Yannick Carrasco to put Atletico ahead in the 20th minute and they ground out the win to preserve their remarkable record of never conceding a goal to Getafe since Simeone became coach nine years ago.
Atletico went into the match after being a dealt a double setback of Kieran Trippier being suspended for 10 weeks for a betting infraction and Diego Costa leaving the club after rescinding his contract.
The absences did not seem to affect them, however, and even though this was far from their most impressive performance of the season, they always looked in control.
A third consecutive league victory took Atletico on to 35 points after 14 games, two ahead of second-placed Real Madrid, who drew 1-1 at Elche and have now played 16 matches.
Getafe, who challenged for a top-four finish in the previous two seasons, are down in 14th place on 17 points, two above the relegation zone.
“It’s not easy to play well in every game and our opponents also played well and needed to pick up points. But even on days when you do not play well, you have to win,” said Simeone.
Atletico captain Koke admitted his side had not been at their best, but hailed their performances throughout the year, in particular since emerging from the three-month coronavirus stoppage.
“We knew who we were up against a difficult team and we weren’t always precise with our passes but it’s three more points, which is what we wanted before the game,” Koke said.
“We’ve had a spectacular year, after the lockdown we underwent a big change and took a step forward in the way we play, working and competing day in day out.”
He also paid tribute to Argentine Simeone, who has transformed Atletico’s fortunes since succeeding Gregorio Manzano in 2011.
“We should congratulate the coach, it’s a lot of years in charge he’s given the team a lot of stability and he’s fundamental to the way we are,” Koke said.