The coach had said there was "no sense" in playing La Liga matches this weekend after the devastating and deadly floods in the Valencia region but his team secured a comfortable victory.
Food and other useful donated products were collected outside the Metropolitano stadium in support of those affected in the east of Spain by the floods which have killed more than 200 people before Giuliano Simeone and Alexander Sorloth's goals earned them three points.
Last weekend Atletico suffered their first defeat at the season at Real Betis and had won just one of their last four La Liga games before beating Las Palmas.
"I'm very happy for my first goal for Atletico but we can't ignore everything that's happening in Valencia, all the victims there. I send my support and strength to them," said Giuliano Simeone.
"To become an idol at the Metropolitano you have to do so many things like all the great players who have been here. I will keep working with humility and enjoy this win, and work in the coming days for the next game in the Champions League (against Paris Saint-Germain)."
Las Palmas goalkeeper Jasper Cillessen saved well from Pablo Barrios, back from injury, in the early stages, while Atletico's Jan Oblak thwarted Fabio Silva.
The hosts took the lead after 37 minutes when Nahuel Molina's long ball found Giuliano Simeone darting in behind the defence.
The striker, deployed on the right wing by his father, burst into the box and swept the ball across Cillessen into the far corner.
As in Saturday's fixtures, the first goalscorer held up a shirt with a message of support to those hit by the flooding, along with captain Koke.
Griezmann hit the crossbar just before the break as Atletico sought to double their lead.
Dutch international Cillessen was taken off on a stretcher after an hour following a clash with Atletico defender Molina, to be replaced by Dinko Horkas.
Sorloth sealed Atletico's straightforward victory in the 84th minute with a clinical finish after being played in by Rodrigo De Paul.
Later Sunday La Liga leaders Barcelona host Espanyol in a derby clash, looking to move nine points clear of second place Real Madrid.
The champions' game at Valencia was postponed because of the flooding, along with Rayo Vallecano's visit to face Villarreal.
