After beating Getafe last weekend by the same scoreline, Atletico have begun the season in familiar fashion, with efficiency trumping invention despite an ambitious set of summer signings.
But two wins out of two already puts them ahead of Barcelona, who have lost to Athletic Bilbao and play Real Betis later on Sunday, and Real Madrid, who were held by Real Valladolid on Saturday.
Joao Felix, Atletico's 126 million-euro ($140 million) signing from Benfica and much-hailed replacement for Antoine Griezmann, was, like last week, rather quiet but, like last week, delivered the match's defining moment.
The 19-year-old's perfectly-timed pass provided the assist for Vitolo while Felix had been picked out by Kieran Trippier, who was faultless again on his second Atletico start.
Leganes did hit the post at 0-0 with a free-kick from Jonathan Silva but lacked the cutting edge required to avoid a second consecutive defeat, after their opening loss at home to Osasuna.
Atletico enjoyed most of the ball in the first half but never really clicked in the final third, where Alvaro Morata and Felix looked like two strikers still finding each other's rhythm.
Every time Felix got the ball he was crowded out, his positioning too fixed and running too predictable, allowing Leganes to swarm around and mark him out of the game.
They were alert as well to Trippier, shutting down the full-back's ability to cross even if one superb ball over the top put Morata in behind but he was unable to bring it down.
Both teams began the second half with added fervour as Felix volleyed over after Kenneth Omeruo was caught napping and Roberto Rosales almost scored an own-goal, his diving defensive header coming back off the post.
In between, Leganes hit the woodwork at the right end too, with Silva's free-kick drifting just away from the top corner before a scramble in the area allowed Javi Eraso to shoot but straight at Jan Oblak.
The game was in the balance with 20 minutes left but Simeone brought Vitolo on for Mario Hermoso and the change paid off.
Trippier started it with a ball down the right wing to Felix, whose beautifully timed pass inside found the run of Vitolo, who tucked it into the corner.
Morata might have made it two but after weaving through, his finish was blocked by the leg of Juan Soriano. Leganes searched for an equaliser as Eraso failed to meet a header before Soriano went up for a corner in injury-time. Atletico held on.