Williams lost to Makarova in straight sets in the fourth round of the 2014 Australian Open.
"I got off to a fast start because I knew she was a really tough opponent and I didn't want to start out slow," Williams said after the match. "I haven't been able play much since Wimbledon, but I was just happy that I was able to make it out here to the Open, so every day I'll just see how it goes."
Serena's sister, Venus Williams was also in action on Tuesday, topping Kateryna Kozlova with a 6-2, 5-7, 6-4 victory.
Fifth-seeded Simona Halep was crisp and sharp in her first match of the U.S. Open.
The Romanian cruised to a 6-0, 6-2 victory over Kirsten Flipkens of Belguim on Tuesday to advance to the second round.
"It was a tough match, because for me the first round of a tournament is always tough," Halep said. "I started pretty well, I played my game today. I had enough time to do what I wanted."
Halep converted 22 winners in the easy victory and will face the Czech Republic's Lucie Safarova, who scored a 6-4, 6-4 victory over Austria's Daria Gavrilova.
Also advancing to the second round was 15th-seeded Timea Bacsinszky of Switzerland, who posted a 6-1, 6-1 victory over Russia's Vitalia Diatchenko. Australia's Samantha Stosur, seeded 16th, won her first-round match, 7-5, 6-7 (4), 6-1, over Italy's Camila Giorgi.
Fourth-seeded Agnieszka Radwanska of Poland had no problems getting past American Jessica Pegula 6-1, 6-1. Radwanska was coming off a tournament win in New Haven, Conn., last weekend.