Maxwell, who has been in good form since the restart of the competition, led his team to victory as he scored an explosive 50 off just 30.
The openers did a fine job as youngster Yashasvi Jaiswal scored 31 runs and Evin Lewis made an impressive 58.
Mumbai Indians were defeated by Royal Challengers Bangalore on Sunday after recording consecutive losses against CSK and KKR earlier.
Virat Kohli became the first Indian player in the history of Twenty20 cricket to go past 10,000 runs in the format.
The IPL 2021 saw Harshal Patel take a hat-trick in the match against Mumbai Indians and it was the 20th instance in the tournament.
Not only did the match see Harshal Patel take a hat-trick, but Virat Kohli also became the first Indian to get 10,000 T20 runs.
MS Dhoni ensured a tidy finish to proceedings in Chennai Super Kings' triumph against Royal Challengers Bangalore on Friday.
Dwayne Bravo delivered the goods with the ball with MS Dhoni and Suresh Raina ensuring a tidy finish to help CSK beat RCB by six wickets.
Virat Kohli admitted that his players needed to step up and deliver the goods, following a second consecutive defeat for RCB in the ongoing UAE leg of IPL 2021.
Dwayne Bravo and Shardul Thakur helped CSK restrict RCB to a total of 156, which is certainly praiseworthy considering the fine performances by Virat Kohli and Devdutt Padikkal.