Griezmann netted an overhead kick in the second half before setting up Kevin Gameiro as Atletico kept alive their hopes of qualifying for the Champions League knockout stages.
The Frenchman's strike, which ended a goal drought dating back to September, sent Diego Simeone's side to six points in Group C, leaving them third but only two points behind Roma with one fixture remaining.
"I'm happy to have scored," Griezmann told Marca. "I'm happy for my teammates, that's how I help them.
"I try to give the best of myself, but we have to work and keep working. It was important to win and then we'll see. We're going to try until the end."