The game looked set for a draw when until 32-year old Glenn Murray came on in the 80th minute.
Ninety seconds after his introduction the English striker stole the winner for the visitors by heading home a corner in the 82nd minute.
Baba's performance was very impressive after setting up Willian and Hazard on a number of occasions with splendid crosses but the attackers just could not connect well to give Chelsea the three points.
The former Augsburg left-back was substituted a few seconds after the goal as Mourinho introduced more attackers to look for the equalizer.
Baba, 21, has been very inconsistent for Chelsea in the English Premier League after only three games in fifteen matches.