Britain’s Daryll Neita produced a fine run to win the women’s 100m in 11.29 seconds, but the US finished first, second and third in the men’s event.
Alexandra Bell, another British athlete, won the women’s 800m but Jake Wightman lost out in a sprint finish to American Josh Thompson in the 1500m.
The two-day event concludes on Tuesday.
Belarus’ Maksim Nedasekau won the high jump by clearing 2.35m, a world lead for 2019, while USA won the final race of the day – the men’s 4x100m relay – in a time of 38.26 seconds.
The quartet consisted of Demek Kemp, Mike Rodgers, Isiah Young and Chris Belcher, although Belcher, who ran the last leg, later apologised for slowing down and celebrating before the end of the race.
He wrote on Twitter: “Just want to take the time to apologize to USA Track and Field, the coaching staff, and my USA teammates for showboating.
“That’s not my style of running and I understand I ruined a chance for us to have a top time in the world for the 4×100. I am truly sorry and will never do it again.”
You get nine points for each event victory and Europe hold a 331-304 lead after 18 of the 37 events.
There will be another 19 competitions on Tuesday, with the final one being a mixed medley relay, with each quartet consisting of two men and two women.
This is the last major event on the athletics calendar before the World Championships in Doha from 27 September to 6 October.