Sonia Bompastor's Chelsea, still bidding for a first Champions League title after four semi-final exits and a final defeat since 2018, made it two wins from two in Group B after beating Real Madrid in their opener.
The five-time defending English champions forged ahead early on, thanks to rising star Agnes Beever-Jones' first goal in the competition.
Japanese forward Maika Hamano caught home goalkeeper Olivia Clark off her line from long range to make it two.
The away side moved further in front with Guro Reiten's second-half penalty, before Nikee van Dijk grabbed a consolation for Twente.
Chelsea are enjoying a fine start to their first season since long-serving coach Emma Hayes left to become boss of the United States national team. They have also won their first three Women's Super League matches.
Earlier, Real Madrid bounced back from their opening loss to Chelsea by thrashing Celtic 4-0.
Scotland international Caroline Weir curled home a brilliant left-footed strike from outside the box into the top corner to give Real Madrid a seventh-minute lead.
The hosts had to wait until the 72nd minute to double their advantage against a stubborn Celtic through Signe Bruun's header.
Caroline Moller came off the bench and added a wonderful third with a 30-yard lob, before Colombian star Linda Caicedo rounded off the scoring with a penalty.
Real Madrid, bidding to avoid a third straight group-stage exit, sit in second place, above Twente on goal difference.
Lyon made it two wins from two in Group A with an impressive 2-0 success at two-time champions Wolfsburg.
France centre-back Wendie Renard opened the scoring in the eighth minute and US Olympic gold medallist Lindsey Horan scored from the spot in the second period.
Last season's runners-up Lyon sit behind Roma in the standings on goal difference and next visit the Italian club in November.
Six different players scored as Roma continued their flying start to Group A with a 6-1 rout of tournament debutants Galatasaray in Istanbul.
