The Arsenal winger scored twice and added an assist as the Gunners brushed aside Monaco at the Emirates Stadium, with Saka involved in all three goals of the 3-0 win.
It was the fifth time Saka has both scored and assisted in the same Champions League match since the start of last season.
As a result, he is now two clear of Phil Foden for such appearances in the competition during that period.
His England teammate has achieved the feat three times across that time.
Meanwhile, a string of players are tied for third with goals and assists in two appearances, including Harry Kane, Jude Bellingham and Vinicius Junior.
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Saka achieved the feat in each of Arsenal's home group matches last term against PSV, Sevilla and Lens.
He has since followed it up this season in their two most recent wins over Sporting Lisbon and Monaco.
In doing so, the 23-year-old now has eight goals and six assists in 14 Champions League appearances.
Only Kane and Vinicius Junior have more goal contributions in the competition since the beginning of the 2023/24 campaign.
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Bukayo Saka joins Mohamed Salah in exclusive club during Arsenal's Champions League win
Saka also joined an exclusive club with his performance against Monaco, having scored his side's first two goals before setting up Kai Havertz for a third.
With nine goals and 12 assists in 21 appearances across all competitions this term, he is alongside Mohamed Salah as the only Premier League players with 20 or more goal involvements.
Mikel Arteta was full of praise for Saka after the match, telling TNT Sports: "He looks really mature.
"What he has already done in the game at his age is incredible. Very humble, a great guy to have around and an incredible talent.
"He's a special person. In his role, his leadership is increasing. With the young kids he is amazing, with the seniors he is amazing. He is loved by everybody and he makes the difference on the pitch."
Meanwhile, the result saw Arteta's side move up to third in the league phase table.
After six matches, the Gunners have four wins, one draw and one loss to their name.
Arsenal will conclude their campaign in January with a home match against Dinamo Zagreb before a trip to face Spanish side Girona.
Beforehand, though, they host Everton in the Premier League on Saturday afternoon ahead of a busy festive schedule.