Melzer pounced on Kendrick's serve in the first set but couldn't maintain the pace. Kendrick took advantage by breaking the Austrian in the first and seventh games of the second set to take a 2-5 lead.
It appeared the match was headed for a third set before Melzer broke back in the eighth game when Kendrick double-faulted and hit an unforced backhand error on the final two points.
Kendrick then double-faulted at break point in the 10th game and fought off one match point in the final game before he hit a backhand into the net on the final point.
"I started rushing. I tried to do too much too early," Melzer said. "On hard court, you have one, two shots in a point. Here, you have to try to be mentally alert."
Melzer lost early at the Sony Ericsson Open in Miami last week and had little time to adjust to the slower clay courts at River Oaks. He was a U.S. Clay Court finalist in 2006 at Houston's Westside Tennis Club, losing to Mardy Fish.
"I felt if I played my game and stayed focused, I would get through," Melzer said. "But he is a good shot maker and it's tough on clay the first time. It's a matter of playing as many shots at the start and I finally found a good rhythm."
Melzer escaped a double break in the fourth game of the opening set to hold serve. Kendrick didn't win a point in serving the fifth game and Melzer broke him again in the seventh game with a forehand winner to wrap up the first set.
Unseasonably low temperatures in the 60s and a steady wind blew across the country club's Stadium Court.
"It was pretty chilly," Melzer said. "I usually don't play in long sleeves when I'm here. The clay is slower and if it's chilly, it's harder."
Melzer is 15-5 in U.S. Clay Court play with appearances in two quarterfinals, two semifinals and losing in the 2006 finals.
"I've done so well since I've been playing here," he said. "My worst finish is the quarterfinals so this is something special. I think I deserve to win."