Kendrick fell behind a break in each set before sweeping past France's Jean-Rene Lisnard, 7-5, 7-5.
"I got down early in both sets, but I never really panicked," Kendrick said. "I wasn't used to his serve at first, but I knew once I got some balls in play I could work the points and move him around."
Kendrick's toughest match this week came in the second round of qualifying, when he rallied from a set and a break down to defeat countryman Michael Russell.
"I'm very excited, I don't know what to say," said Kendrick, a 23-year-old from Florida. "I felt like I've played this well in Challenger tournaments before, and it's just a matter of doing it in tour events as well."
Up next for Kendrick will be Vladimir Voltchkov of Belarus, who moved on when Armenia's Sargis Sargsian retired due to muscle cramps. The players split the first two sets and Voltchkov won the opening game of the third.
"I think everyone could see he was in pain," said Voltchkov, who received treatment earlier for a sore right elbow. "I saw him after the match in the locker room and he was in pain. Anyone who knows Sargis knows he's tough, so he must have been in quite a bit of pain."
Fourth seed Jan-Michael Gambill dispatched fellow American Justin Gimelstob, 7-5, 7-5.
Trader Joe's: Car crashes into Long Island store, injuring 11
Reindeer recovered after escaping from Santa during lighting ceremony