Lille opened the scoring through a Burak Yilmaz penalty on 38 minutes to cut their aggregate deficit to 2-1, but Pulisic provided a cool finish on the stroke of half-time to restore Chelsea's two-goal cushion.
Chelsea played the tie amid the club's potential sale. UEFA had to seek clarification from the European Union that the fixture could go ahead after they followed the U.K. in sanctioning Abramovich on Tuesday.
Lille had made the better start to the match.
Lille were rewarded in the 38th minute when they were awarded a penalty following a VAR review after a Jorginho handball in the area.
The 36-year-old Yilmaz, the third oldest scorer in the Champions League knockout stages after Paolo Maldini and Ryan Giggs, buried the spot-kick into the top corner to give the hosts a deserved lead and high hopes of an upset after losing the first leg 2-0 at Stamford Bridge.
Lille, who had not conceded a goal in their three Ligue 1 games since the first leg, let their guard down, however, and Chelsea punished them with their first shot on target as Pulisic collected a fine through ball from Jorginho to score with a low shot three minutes into first-half stoppage time.
The goal meant Pulisic tied Javier "Chicharito" Hernandez for most goal in the Champions League by a CONCACAF international.
Chelsea were far more ruthless and after 71 minutes Mount's cross bounced off Azpilicueta's knee into the top corner to end Lille's hopes of reaching the quarterfinals.
Information from Reuters contributed to this report.