"Pals at the Emmys," Winkler captioned the photo, which features him and the Oscar-winning filmmaker dressed in formal wear and smiling.
Howard re-tweeted the picture and added the message: "My friend's win is so deserved and great. ! Bravo @hwinkler4real."
Winkler, 72, won his first Primetime Emmy -- the Best Supporting Actor in a Comedy honor -- for his work in Barry, which recently wrapped its first season.
Happy Days initially aired 1974-84 and has remained popular in re-runs ever since.