Bayern's shock 3-2 defeat to Rostov earlier on Wednesday meant Atletico needed just a point to win the group.
Already assured of their place in the last 16, Bayern's shock 3-2 defeat to Rostov earlier on Wednesday meant Atletico needed just a point to win the group.
And Diego Simeone's men were rarely troubled as two goals in 11 second-half minutes from French international duo Gameiro and Griezmann ensured Atletico remain the only side with a 100 percent Champions League record this season.
Simeone can now afford the luxury of resting his key men for the trip to Munich on December 6, whilst PSV must beat Rostov at home to progress into the Europa League.
"I'm delighted because with a game to spare we are first in a difficult group," said Simeone.
"We dealt with the games away from home in Russia and Holland very well."
Still smarting from a 3-0 defeat to bitter rivals Real Madrid on Saturday, Simeone made four changes in a bid to rediscover the defensive solidity that has defined his hugely successful five years in charge.
The Argentine was rewarded with a first clean sheet in six games, whilst Gameiro took his chance after replacing the hapless Fernando Torres up front.
"During the season there are different moments that you have to live with, but the important thing are the objectives you set and how you end the season," added Simeone.
"There will be criticism and compliments, but you can't focus on either of those, but on the objectives at hand."
Gameiro should have opened the scoring just eight minutes in when he met Yannick Carrasco's tantalising cross, but somehow shanked his finish well off target from point blank range.
Diego Godin headed another good opening too close to PSV 'keeper Jeroen Zoet, but the visitors could have gone in front but for brilliant defensive work from Griezmann midway through the first half.
Euro 2016's top scorer raced back as Atletico's last defender to ensure Gaston Pereiro couldn't get a clean strike and goal and Jan Oblak comfortably collected.
Atletico had to wait until 10 minutes after the break to make the breakthrough as Griezmann fed Gameiro on the right side of the area and he drilled a low shot in off the far post.
The hosts put the game to bed 24 minutes from time when Griezmann latched onto Tiago's through ball and made the most of a stumble by Zoet to fire home his first goal in three games at the near post.
Gameiro was then unfortunate not to add his second of the night when a thumping header from Koke's corner came back of the bar.