The Danish champions made a flying start at Køge Idrætspark, taking the lead after just nine minutes through American defender Macy Schultz. She brilliantly flicked Mille Gejl’s free-kick into the far corner with her heel to give the hosts a 1–0 advantage.
HB Køge doubled their lead before the half-hour mark when Nadia Nadim headed home a precise cross from Kyra Carusa.
The hosts then extended their advantage in the 35th minute after Servette defender Noémie Carage inadvertently turned the ball into her own net, leaving HB Køge 3–0 ahead at the interval.
Servette responded strongly after the break and pulled one goal back in the 48th minute through Laia Ballesté, who headed past the HB Køge defence.
However, the Swiss champions' hopes of a comeback were ended in the 64th minute when Kyra Carusa headed in another Mille Gejl free-kick to restore HB Køge's three-goal advantage.
Servette came close to reducing the deficit again when Meriame Terchoun struck the post in the 76th minute, but HB Køge remained in control.
Substitute Emelía Óskarsdóttir completed the rout two minutes from full time, finishing a counter-attack to make it 5–1.
The victory is particularly significant for HB Køge, as it represents the first win for Danish women's football in the Champions League league phase since the competition adopted the group-stage format in 2021/22.
HB Køge had opened their league-phase campaign with a narrow 1–0 defeat away to Arsenal, while Servette suffered an 8–0 loss to OL Lyonnes in their opening fixture.
Full-time result
• HB Køge Women: 5 – Macy Schultz 9', Nadia Nadim, Noémie Carage (og) 35', Kyra Carusa 64', Emelía Óskarsdóttir 88'
• Servette FCCF: 1 – Laia Ballesté 48'
HB Køge will next face defending champions Barcelona at home on 29 October, while Servette will host OH Leuven on the same matchday.