With both sides looking for their first win of the new La Liga season, it was Diego Simeone's men who came out on top, scoring twice in the first 5 minutes and three times in the second half after a brief attempt at a comeback to condemn Las Palmas to their second loss of the season as the game ended 5-1.
Atletico were without Antoine Griezmann, with the striker undergoing a two-game suspension, but the team were unaffected by his absence.
The side from the Spanish capital scored with the first effort on goal of the game, as Angel Correa received the ball from Lucas Vietto, used his quick feet to create a little bit of room for himself and fired the ball low into the right corner.
Just two minutes later on their next attack, Yannick Carrasco doubled the visitors lead as he made his way into the box after being released by Saúl, shifted the ball onto his left foot and drilled his shot across Chichizola into the goal.
After a rapid start to the game, things quietened down as Atletico's solid defence frustrated their opponents and limited them to speculative efforts. Oblak was called into action for the first time in the game as he palmed away a long-range effort from Jonathan Viera.
With the ball spending most of the time in the middle of the park, neither side were able to create any guilt-edged chances before the referee blew his whistle bringing the half to a close.
The second half started in much of the same fashion, with Atletico managing to keep the home side at arm's length as they failed to really trouble Oblak in the visitors' goal.
However, Jonathan Calleri brought Las Palmas back into the game on the 58 minute mark with his first goal for the club after joining on-loan in the summer. A brilliant cross in from the left by Momo was met by the Argentinian striker, who rose high to head the ball past Jan Oblak.
The home side looked to be playing with more purpose directly after the goal but the brief hope of a comeback was short-lived. A clearance from Pedro Bigas fell straight at the feet of Koke at the edge of the box and the Spaniard expertly curled the ball into the top corner, leaving Chichizola with no chance.
The quick Koke response evidently knocked the stuffing out of Las Palmas and the home side didn't create any real opportunities before Koke extended his side's lead once again. Carrasco set off on a mazy dribble into the box before being tackled by Mauricio Lemos and with the ball in the air, Koke reacted with an acrobatic effort from close range to give his side an insurmountable lead.
Jonathan Viera had the chance to reduce the deficit for the home side after being brought down by Gabi in the penalty area but responded with a weak penalty which Oblak kept out, diving down to his right and making the save.
Thomas then compounded matters for the hosts as he was afforded way too much time at the edge of the box after Carrasco cut the ball back to him and the Ghanaian midfielder guided the ball into the corner for his side's fifth goal.
Atletico were solid throughout and much improved from last week's draw against Girona, as they were able to secure Diego Simeone's first win of this La Liga campaign.