Game. Set. Smash.

Here it is ... proof Drake and Serena Williams are officially a thing -- making out at a fancy Cincinnati restaurant Sunday night ... and TMZ has the pics.

Hours after Serena dominated and won the WTA tournament in Cinci -- with Drake in the crowd -- the two hit up the uber-fancy Sotto restaurant in downtown for some hoity-toity Italian food (the porterhouse is $85).

The two had a private room in the back of the eatery -- where they couldn't keep their hands and lips off of each other ... while several patrons watched.

People inside the restaurant tell us the two were joined by 6 other people ...and at one point ordered a round of tequila shots for the table.

There have been rumors about the two hookin' up for months -- ever since Drake was spotted cheering for Serena at Wimbledon -- but now the pics confirm it ... it's game on.