Bournemouth had already taken the lead from a penalty on Thursday (Friday AEDT) when Maignan was shown a straight red card and conceded another spot kick by putting his gloves in the face of US midfielder Tyler Adams and pushing him to the ground.
Marcus Tavernier converted the second penalty against substitute goalkeeper Lorenzo Torriani to double the home side's lead, and there was no way back for Milan after that. Substitute Amine Adli made it 3-0 late with a perfectly executed curling free kick.
Four other teams also have three wins from three, including Bayer Leverkusen, after Jonas Hofmann scored twice in a three-minute span to secure a 2-0 victory at OFI Crete.
But Juventus were held to a 2-2 draw by Rennes after having a late winner ruled out for offside.
Hofmann netted his double late in the first half as Leverkusen continued their good start under new coach Carles Martínez, who has now overseen seven wins from eight games across all competitions since starting with a shock loss to Elversberg.
Ferencvaros also stayed perfect after a 4-1 victory over Portuguese second-division side Torreense.
In a clash of unbeaten teams, Benfica won 4-1 at Omonia, while Olympiacos needed a late own goal to secure their third straight win, 1-0 win over Sparta Prague.
Nick Woltemade converted from the spot in the 67th minute to salvage a 2-2 home draw for Juventus against Rennes, but the hosts had a potential winner by Jhon Lucumi ruled out by VAR.
It was Woltemade's third goal in three games in the competition after joining on loan from Newcastle.
The Bianconeri pressured early and took the lead after Zeki Celik collected a through-pass from Woltemade.
But Musa Al-Taamari equalised and Boulaye Dia calmy gave the visitors the lead from the spot, sending Juve goalkeeper Guglielmo Vicario the wrong way.
Like Juve, Sunderland hoped to make it three wins from three on a trip to Lech Poznan. Forward Timur Tutierov put the Premier League side ahead with a header for his first Europa League goal in the second minute, but substitute Leo Bengtsson made it 1-1 in the second half to earn a first point for the Polish club.
In other results, Crystal Palace drew 2-2 with 10-man Besiktas, Celtic lost 2-1 at home to Celta Vigo, Hoffenheim got their first points with a 3-0 win over Ligue 1 leaders Lyon, and Real Sociedad had the biggest win of the night, 6-0 at Lillestrom.
Earlier, Marseille recorded a third straight loss, 1-0 to Sturm Graz, while Union Saint-Gilloise routed Israeli champions Hapoel Beer-Sheva 4-0. That game was played without fans in Dusseldorf, Germany, after authorities in Leuven, Belgium, refused to host it due to public safety concerns.
In Istanbul, Palace's Yeremy Pini cancelled out Besiktas's opening goal by Wilfred Ndidi, and Jean Philippe Mateta pushed the English team ahead before Junior Olaitan levelled again.
The English side failed to make use of a one-man advantage after Umit Akdag was sent off 13 minutes from time.
Czech provincial side Jablonec kept high-scoring Brighton at bay in a 0-0 draw in the Conference League, while former Liverpool striker Mohamed Salah marked his 150th game in European competitions by scoring again for Tranbzonspor in a 2-0 win over Hearts.
It was the second goal for Salah in the competition after netting in the previous 4-2 win away at KuPS Kuopio.
