Chelsea, who welcomed 2,000 fans back to Stamford Bridge after coronavirus restrictions were eased, went ahead as Zouma headed in from Mason Mount's corner.
Romelu Lukaku, making his first home appearance since his return to the club, scored two fine goals either side of an opportunist effort from Mateo Kovacic as both players registered their first-ever goals at Stamford Bridge.
Chelsea were held to a 1-1 draw against FC Krasnodar in the Champions League on Tuesday night at Stamford Bridge. Frank Lampard's side came from behind to draw their final group to extend their unbeaten run to 17 games in all competitions.
Michy Batshuayi scored a hat-trick as Chelsea eased past Championship side Nottingham Forest to book a place in the fourth round of the Carabao Cup. Brazilian winger Kenedy tapped home to make it 1-0 at Stamford Bridge.
In the second-half, Werder Bremen's Lennart Thy scored to make it 3-2 but Pedro wrapped up the victory in the dying moments. Chelsea start their Premier League campaign against West Ham on August 15 at Stamford Bridge.
The midfielder, who netted his first UCL goal during Chelsea's 3-1 defeat of Sporting Lisbon in October 2014 at the Stamford Bridge, only have to play a couple of games to become the Nigerian player with highest appearance in the European competition
Cole Palmer's first-half penalty gave Chelsea a narrow win over West London rivals Fulham at Stamford Bridge in the Premier League. Palmer's reverse pass set up Raheem Sterling, who was caught by Issa Diop inside the penalty area.
Chelsea moved to within one win of the Premier League title and confirmed Middlesbrough's relegation with a consummate performance and emphatic victory at Stamford Bridge.
Chelsea secured a narrow 3-2 win over Bristol Rovers in the EFL Cup second round on Tuesday night as Michy Batshuayi scored two goals on his first start for the Blues at Stamford Bridge.
Brentford became the first side in the Premier League era to win their first three matches at Stamford Bridge as Ethan Pinnock and Bryan Mbeumo earned them a 2-0 victory over Chelsea.