Justin Kluivert and Marcus Tavernier converted first-half penalties to put Bournemouth firmly in control against AC Milan, one of Europe’s leading clubs.
Milan goalkeeper and skipper Mike Maignan was red carded early on for a foul on Tyler Adams and his side never fully recovered.
Amine Adli scored a sublime 84th free-kick to make it 3-0, the Premier League side having opened their inaugural Europa League campaign with victory at Real Sociedad followed by a 3-0 home win over Sturm Graz last week.
Bournemouth, who became the first English club since Sunderland in 1973/74 to win the first three European fixtures in their history, will now face Sparta Prague and Celta Vigo in November.
“It means a lot. We came off two victories, so that gave us a good feeling for this game,” Kluivert told TNT Sports.
“We trust ourselves. It doesn’t matter who we play against. We know what we’re capable of, and I think we showed that today.”
Bournemouth’s Premier League rivals Crystal Palace rebounded from a 5-0 weekend thrashing by Brighton to claim a 2-2 draw with Beskitas in Istanbul, while Scottish giants Celtic suffered a third successive defeat, going down 2-1 to Celta Vigo.
Bayer Leverkusen, however, also made it three straight wins with a Jonas Hofmann double earning a 2-0 away win at OFI Crete as both Juventus and Sunderland lost ground in Thursday’s third matchday.
The once mighty Hungarian side Ferencvaros kept pace with Leverkusen on nine points thumping Portuguese outfit Torreense 4-1, while Belgium’s Union Saint-Gilloise won 4-0 against Israeli outfit Hapoel Be’er Sheva.
Saint-Gilloise, Sunderland and Juve all have seven points from three games.
Juventus thought they had come from behind to beat French side Rennes but had their late ‘winner’ ruled out for a marginal offside.
Zeki Celik put Juve ahead after five minutes only for a poor clearance 10 minutes later allowing Musa Al-Taamari to poke home an equaliser. Jut before the break Boulaye Dia put the visitors ahead.
Juventus made it 2-2 thanks to a handball and a spot-kick transformed by Nick Woltemade before VAR provided the biggest talking point, disallowing Jhon Lucumi’s 88th minute strike.
Clad in a new all-pink kit, Sunderland were left kicking themselves after a 1-1 draw in Poland.
The Blacks Cats took a second minute lead in Poznan thanks to Timur Tutierov and dominated the game without being able to close out the win.
With two home games remaining, however, the second round still beckons for Regis Le Bris’ side.
Marseille went down 1-0 to Sturn Graz while Lyon suffered a 3-0 thrashing at the hands of Hoffenheim.
In the Conference League, former Liverpool striker Mohamed Salah opened the scoring from the penalty spot in Trabzonspor’s 2-0 win over Scottish side Hearts.
Brighton were held to a 0-0 draw at Czech side Jablonec, as Monaco thumped Freiburg 3-0 and Ajax snuck a 2-0 win over Atalanta. (AFP)