The Briton qualified on pole before being demoted to third after receiving a two-place penalty for crossing the pitlane exit line.
But she made it past a poor-starting Nerea Marti off the line before swooping past Visser, who had inherited pole, around the inside of Turn 3.
Holding off the Dutch driver’s challenge after two safety-car periods, Chadwick maintained her perfect score for this season.
Visser fell to fourth towards the end of the race, with Belen Garcia taking second for her first series podium, with Marti securing third having started second.
There was a lap one safety car after Abbie Eaton, Marta Garcia and Belen Garcia made contact off the line, with Scuderia W driver Eaton attempting to move through the inside of the pair before making contact.
The incident ended Eaton’s race, with Marta Garcia dropping to seventh while Belen Garcia emerged unscathed in third.
Racing resumed with 20 minutes left on the clock, with Chadwick resisting Visser on the restart before quickly building up a healthy lead.
But racing was immediately neutralised once more after Chloe Chambers and Emely de Heus collided at Turns 3 and 4, the latter having tried to dive down the inside and receiving a 10-second stop/go penalty for the incident.
The safety car was deployed for five minutes, with Visser closing in on Chadwick on the main straight on the restart, briefly taking the lead on the inside of Turn 1 before the double champion retook the top spot around the outside of Turn 2.
Belen Garcia then made it past Marti to take second, while Alice Powell and Fabienne Wohlwend battled for fifth further back, the Briton taking the position having charged through the field from 11th.
Chadwick had a 1.5-second lead by lap eight of 13, with Marti claiming third at Turn 11 after Visser ran wide.
From there, the Briton dominated, setting a fastest lap that was 0.5s quicker than Belen Garcia in second and, though the Quantfury Racing driver responded the following tour, Chadwick went on to finish 2.3s ahead.
Powell sealed fifth, with Marta Garcia settling for sixth after the early contact with Eaton, and team-mate Wohlwend in seventh.
Sarah Moore took eighth, with fellow Britons Abbi Pulling and Jess Hawkins rounding off the top 10.
