Quincy Promes headed the Dutch side ahead after 18 minutes before Edson Alvarez scored to put them two goals up five minutes after the interval.
Nicolas Tagliafico dented Lilles chances of launching a comeback with the hosts third of the evening thanks to Hakim Ziyechs assist.
Thats when you need players to move up quickly towards their goal, but we did it too quickly at times. We discussed beforehand that we might need to put the brakes on a bit so as not to lose possession again and get caught out.
The Nigeria international was on parade for the entire duration as Andre Onana put in a fine shift to stop the Great Danes.
Following this defeat, Lille sit at the base of Group H and they would be seeking redemption when they welcome Chelsea to Stade Pierre-Mauroy on October 2.
Before then, they take on Rennes, Strasbourg and Nice in their next three French top-flight fixtures.
Osimhen boasts five goals in five league appearances to lead the goalscorers chart alongside Lyons Moussa Dembele.
Ajax vs Lille LIVE: Stream, score, TV channel and teams for Champions League group game
Goals from Quincy Promes, Edson Alvarez and Nicolas Tagliafico saw off a spirited Lille side, who came into the match following the arrest of over 300 of their supporters after unrest earlier in the day.
The away supporters were arrested close to the Johan Cruyff Arena hours ahead of the Group H match, with the ANP national news agency reporting that fans were walking along the metro lines, forcing officials to halt rail traffic and evacuate two stations for a short while.
Osimhen joined the Great Danes on a five-year deal from Belgian First Division A club Sporting Charleroi as a replacement for Arsenals Nicolas Pepe.
Erik ten Hags side top the group after the impressive win, level on three points with Valencia following their 1-0 victory over Chelsea at Stamford Bridge, and comes despite the loss of star players Frenkie de Jong and Matthijs de Ligt in the summer.
Lille host Frank Lampards men in their next fixture billed for October 2, while Ajax travel to Mestalla for a date with the Spaniards.
“We wanted to take all three points and get off to a good start,” said Promes, a close-season signing from Sevilla.
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“Given the performances last season, the bar was set high, and people were asking if we could do it again this season. I think a 3-0 victory shows that we can.”
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A frantic first half saw both sides hit each other with attack and counter-attack, and the hosts thought they had grabbed a 13th-minute lead when Hakim Ziyech brilliantly took Dusan Tadics pass and fired off a powerful shot, only for the Moroccan to watch in anguish as the ball rattled out off the post and bar.
However they had a deserved lead five minutes later, the impressive Promes beating a dawdling Lille defence to Tagliaficos looping cross and glancing the opener in off the post.
Ajax vs Lille LIVE: Uefa Champions League 2019-20 commentary live stream, TV channel, score, prediction
Promes, a summer signing from Sevilla, then had a great chance to double Ajaxs lead four minutes before the break as he charged onto a pinpoint long pass from Alvarez, but couldnt get enough on his volleyed finish to send it over Lille stopper Mike Maignan.
However they only went in ahead at half-time thanks to keeper Andre Onana, who pulled off an excellent save from Jonathan Ikone before Victor Osimhen spooned over the rebound.
Alvarez doubled the Dutch champions lead five minutes after the restart when he collected a superb David Neres pass and fired home from a tight angle.
Lille pushed and could have pulled one back through Jonathan Bamba before Tagliafico sealed the three points with a bullet header just after the hour mark to leave a frustrated Lille bottom of the group and home fans dreaming of another year of European drama.
“It was a fantastic night for Ajax and the fans, we played against a very good Lille side, we made a few mistakes that almost cost us dear but fortunately our goalkeeper was there to save us because we put ourselves in difficult situations,” said Ten Hag.
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“We have to be more vigilant in our weak moments in the rest of the competition, but I am happy with my team, which at times played fantastic football.”