The result to moved Diego Simeone’s outfit to within two points of Jorge Sampaoli’s third-placed side in the La Liga standings.
The France international delivered a cross from a free kick for Diego Godin to head in the opener in the 37th minute then sent the ball fizzing in off the bar from a set-piece in the 61st.
Spanish midfielder Koke then tapped in the third after Juanfran’s effort was parried by Sergio Rico in the 77th to seal a third straight league win for Atletico.
Joaquin Correa scored a consolation goal for Sevilla in the 85th.
They have failed to win any of their last four games in all competitions and lost their last two, and went out of the Champions League following a 2-0 defeat at Leicester City on Tuesday.
Los Blanquirrojos have 57 points while Atletico are now just two behind them in fourth place.