Kenya's Lawrence Cherono led home the men's race in 2:07.57 with his compatriot Kenneth Kipkemoi in third behind Lelisa Desisa Benti from Ethiopia. The second place finisher, two-time victor Lelisa Desisa, finished one second slower, according to race officials.
Fionnuala McCormack ran a personal best at the Boston Marathon and only just missed out on qualification for Tokyo 2020 - barely six months after having a baby.
Degefa's only other marathon experience might have been on the flat roads of Dubai, but the 28-year-old - whose PB of 2:17:41 from January puts her fourth on the world all-time list - wasn't put off by Boston's hills.
Schulte, 40, was first to arrive at the finish line on Boylston Street, in a time of 2 hours, 36 minutes and eight seconds.
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USA's Jordan Hasay was third in 2:25:20, Ethiopia's Meskerem Assefa fourth in 2:25:40 and defending champion Desiree Linden fifth in 2:27:00.
Seven American runners finished in the top 20 of the men's race, with Scott Fauble leading the way in seventh place.
The elite women's race was a different story.