Master of the late goal this season, Diego Simeone’s men took the opening 10 minutes to find their feet here, but once they did, Slovan struggled to cross the halfway line.
The opener duly arrived just beyond the quarter-hour when Samuel Lino found Julian Alvarez, and the Argentina international opened his body up and curled exquisitely into the top corner for his 12th Champions League goal.
Even a one-goal deficit looked insurmountable based on Slovan’s recent form in this competition, but star player Tigran Barseghyan nearly earned the visitors a stunning equaliser when a rare foray forward from the Sky Blues resulted in the Armenian rattling the crossbar.
Barseghyan limped off injured just eight minutes later, and to compound matters, Atleti doubled their advantage before the break.
Pablo Barrios’ long ball to the back post found the run of Marcos Llorente, who squared for Antoine Griezmann to head home and give his side a comfortable lead.
However, just six minutes into the second half Atleti’s lead was halved from the penalty spot. Clement Lenglet’s efforts to clear a cross led him to taking David Strelec out, and the Slovan forward picked himself up to convert from 12 yards after a VAR review.
That spread anxiety around the Metropolitano, but the talismanic Griezmann calmed nerves when restoring his side’s two-goal lead just five minutes later.
Koke drove the ball into the area to find the Frenchman, who spun and bobbled an effort in at the near post to stifle the Sky Blues’ recovery.
Damage limitation appeared to be the order of the day for Slovan after that, with Alvarez, Lino and Griezmann all going close to scoring a fourth for the hosts.
That deadly trio was then substituted to the visitors' relief with just under 20 minutes remaining - a clear signal that Atletico had taken their foot off the gas ahead of their clash with Getafe at the weekend.
That approach nearly cost Simeone’s men as Jan Oblak denied Slovan a second goal, but the Slovakian visitors had no way back as they became the first side since domestic rivals Zilina to lose all of their first six games in the UCL on debut.
Consequently, their chances of progression are over, white Atleti have entered the race for automatic qualification to the last 16.