The victory makes the 15-time champions the first team since the rebranding of the competition in the early 1990s to reach 200 wins.
And it gave former Madrid playing standout Xabi Alonso a victory in his Champions League debut as the club's coach.
Timothy Weah put visiting Marseille ahead early on but Mbappé struck back from the penalty spot in the 29th and 81st minutes.
The first penalty came after a foul on Rodrygo and the second for a handball by a defender.
Mbappé now has 50 goals in 64 matches with Madrid.
"We are happy that he keeps scoring goals and has been feeling more and more comfortable," Madrid midfielder Federico Valverde said.
"Our job is to make sure the ball gets to him and that he can have even more scoring opportunities than he is having now."
In other matches, an early own goal from keeper Luiz Junior gave Tottenham a 1-0 win over visiting Villarreal.
The victory came on a night when Thomas Partey played before an appearance in court for rape and sexual assault charges.
Thomas Frank's Spurs claimed three points on their Champions League return after the visiting keeper spilled Lucas Bergvall's fourth-minute cross in comical fashion.
But it was Villarreal teammate Partey who later took centre stage.
The former Arsenal midfielder was introduced with 12 minutes left to loud boos a month on from his appearance at Westminster Magistrates Court where he was charged with five counts of rape as well as a charge of sexual assault.
The lawyer for Partey, Jenny Wiltshire, has previously said he "denies all the charges against him" and he is due in court again on Wednesday morning - a matter of hours after the Champions League tie.
Meanwhile, Borussia Dortmund and Juventus drew 4-4 in Turin and Qarabag came from two goals down to win 3-2 at Benfica.
At Athletic Bilbao, Viktor Gyokeres was off target in his Champions League debut for Arsenal.
The London club's substitutes were decisive, though, in a 2-0 win for the Gunners.
Gabriel Martinelli scored less than a minute after he came on and Leandro Trossard — who had replaced Gyokeres — doubled the lead 15 minutes later.
Gyokeres — Arsenal's prized signing who scored six Champions League goals for Sporting Lisbon last season — missed a golden chance shortly after the break.
The Sweden international evaded his marker with ease and rose to meet a well-placed free kick from Declan Rice but his header went well wide of the target.
In the second season of the new league-phase format, the top eight teams advance to the round of 16. The next 16 teams enter a two-leg playoff, with eight advancing.
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