Errani, ranked No. 5 in the world, becomes the fifth of the tournament's eight seeds to lose in the first two rounds of the final WTA tuneup before next week's U.S. Open.
Errani had trouble with her slow, spinning serves all afternoon and was broken four times by the 25-year-old Russian.
Makarova will play Romanian Simona Halep in the quarterfinals.
Halep dropped her first set Wednesday but bounced back for a 3-6, 6-4, 6-1 win over Carla Suarez Navarro of Spain.
The three remaining seeds — defending champion Petra Kvitova, four-time New Haven champion Caroline Wozniacki and American Sloane Stephens — each had second-round matches scheduled later Wednesday.