Chelsea qualified for the Champions League despite losing 2-1 at Aston Villa in the Premier League on Sunday as they pipped Leicester City to a top-four spot by one point.
Thomas Tuchel's Chelsea, who had Ben Chilwell on the scoresheet in reply to goals by Bertrand Traore and an Anwar El Ghazi penalty, had to rely on London rivals Tottenham Hotspur who beat Leicester 4-2 away.
Chelsea meet Premier League champions Manchester City in the Champions League final in Porto, Portugal next weekend but wanted to secure their spot in the competition beforehand.
The visitors dominated the first half against Villa, with 68% of possession, but it was their former forward Traore who grabbed the advantage for the home side, hitting the target off the underside of the bar from a Jack Grealish corner.
Chelsea should have equalised through Christian Pulisic before Traore won a penalty in the 51st minute when Jorginho clipped his ankle in the box and brought him down. Dutch midfielder El Ghazi scored from the spot.
Chilwell pulled a goal back for Chelsea in the 70th minute from a Pulisic pass, 10 minutes after Timo Werner had a goal ruled out for offside against captain Cesar Azpilicueta.
Azpilicueta was sent off in the 88th minute after reacting to a Grealish challenge by barging him in the face.
Chelsea started the day in third spot but Liverpool overtook them with a 2-0 home win over Crystal Palace. Chelsea will be concerned for first choice goalkeeper Edouard Mendy who had to be sustituted at halftime after falling heavily into the post.