Davidson got 20 points and 15 rebounds from Andrew Lovedale while improving to 3-1. The Wildcats' lone loss has been to nationally-ranked Oklahoma.
The Wildcats made 13-of-32 three-point shots and hit 49.3 percent of their attempts from the field.
Winthrop (1-3) was led by Cameron Stanley with 20 points. The Eagles have dropped three straight after a season-opening win over North Greenville.
Davidson owned a 41-35 halftime lead and opened the second period on a 14-5 run.