The former Barcelona midfielder had spent most of previous day in meetings with club officials
Belgian winger Carrasco broke the deadlock at the end of the first half, pulling off a classy backheel to knock the ball through the legs of Ter Stegen and keep his composure in front of goal after the German had charged out of his area.
Marcos Llorente nearly gave them an early lead when his shot crashed off the bar, while it took a brilliant save from Ter Stegen to keep out a vicious distance strike from Saul Niguez.
Atletico moved up to second in the standings, level on 20 points with leaders Real Sociedad.