Carter sprinted to victory in a season's best time of 9.96 seconds in a race that saw American Michael Rodgers disqualified on Thursday.
Rodgers – leader of the season's rankings in the 100m sprint – was punished for a false start.
Trinidad and Tobago's Keston Bledman (10.09secs) ran second, with Brit Chijindu Ujah (10.10secs) next best.
Adam Kszczot's victory was one of the main stories of the day as he won the men's 800m in a time of one minute 45.25secs.
The Polish runner was just ahead of Djibouti's Ayanleh Souleiman (+0.24secs) while Botswana's Nijel Amos – who won the silver medal in the same event at the 2012 London Olympics – could only manage fifth.
American Allyson Felix triumphed in the women's 200m in a time of 22.85secs as she continued her excellent season.
Fenix – who holds the Stockholm record of 21.88secs, set in 2009 – just edged compatriot Tori Bowie (+0.06secs) for victory.
Olympic champion Sally Pearson of Australia was disqualified in the women's 100m hurdles, won by American Queen Harrison (12.66secs), while the latter's compatriot, Jennifer Simpson, was triumphant in the women's 1500m.
Jamaican Novlene Williams-Mills also won the women's 400m in a time of 50.09secs.
American Michael Tinsley claimed the men's 400m hurdles in 49.60secs and Ethiopian Muktar Edris edged Kenyan pair Thomas Pkemei Longosiwa and Caleb Mwangangi Ndiku in the men's 5000m.
Other Diamond League events in the men's division saw American Reese Hoffa, South African Godfrey Khotso Mokoena and Finland's Antti Ruuskanen win the shot put, long jump and javelin throw respectively.
In the pole vault, Olympic and European champion Renaud Lavillenie suffered a surprise defeat after failing three times to clear 5.60m. Greece's Konstantinos Filippidis won the event.
Ethiopian Hiwot Ayalew was successful in the women's 3000m steeplechase, while Russian Mariya Kuchina was best in the women's high jump.
And American Tianna Bartoletta and Croatian Sandra Perkovic won the women's long jump and discus throw respectively.