The French forward was instrumental in his side's victory, opening the scoring in the 23rd minute with a neat finish after receiving a pass from Marcos Llorente.
Valencia thought they had equalized through Hugo Duro, but his effort was disallowed by VAR for a foul by Dimitri Foul earlier at the other end of the pitch.
Atletico continued to push for more goals and doubled their lead early in the second half through Carrasco's close-range finish. Lemar completed the scoring in the 72nd minute, heading home from Alvaro Morata's cross.
The win saw Atletico strengthen their hold on third place in the La Liga table, moving six points clear of fourth-placed Real Sociedad with a game in hand. Diego Simeone's side have won five of their last six league matches, showing the kind of form that saw them win the title last season.
Meanwhile, Valencia remain in trouble near the bottom of the table, sitting in 17th place with only a goal difference keeping them above the relegation zone. Ruben Baraja's side have struggled for consistency this season and their away form has been particularly worrying, with only one win in 14 matches on the road.