Coming off his first Grand Slam championship match, ninth-ranked Berdych battled heat and humidity as well as a 514th-ranked Russian opponent whose first win of the year came Monday at the 1.4 million-dollar hardcourt event.
Tursunov, who missed most of last year with an ankle injury, broke Berdych's first service game for a 2-0 lead, but Berdych broke back in the next game and the first set went to a tie-breaker that the Czech dominated.
The Russian answered with the only break of the second set but was broken in the second and fourth games of the final set as Berdych advanced to Thursday's third round, where he will face Kazak Andrey Golubev.
Argentina's David Nalbandian, a former world number three in his first ATP event since April due to a left hamstring injury, snapped a five-match losing streak to Swiss Stanislas Wawrinka by 6-1, 6-3 to reach the third round.
"I played great, just a few mistakes, much better than the match before," Nalbandian said. "I feel good, 100 percent ready to be on court more.
"I'm physically good, maybe not 100 percent with confidence but when I'm physically good I can make it. It's good to know I don't need a lot of matches to feel good."
Wild card entrant Nalbandian, the 2002 Wimbledon runner-up, helped Argentina beat Russia last month to reach the Davis Cup semi-finals and kept himself on a path for a possible quarter-final against US second seed Andy Roddick.
Nalbandian, who plays another Swiss foe next in Marco Chiudinelli, had taken only one set off Wawrinka since his most recent prior victory over him in the first round of the 2006 French Open.
"All matches are different," Nalbandian said. "Always I play tough against him. It doesn't matter the score. Every time we know each other a little better. Maybe that's why (I won)."
Serbian Janko Tipsarevic blasted 16 aces to oust US sixth seed Sam Querrey 7-6 (7/3), 6-3 in a rematch of a Los Angeles semi-final in which Querrey saved a match point and rallied to win on his way to capturing the title.
"My serve usually helps me. Today was a little more than I expected," said Tipsarevic, who won 29-of-31 first-serve points and 20-of-24 on second serves.
"I was serving much better. I won my games more easily, not running and grinding for my points, so I was fresher for the return. I'm so happy with these conditions I was able to close it out in two sets."
Tipsarevic will next face Colombia's Alejandro Falla, who led 7-5, 3-2 when Australia's Lleyton Hewitt retired with a sore right calf muscle.
"I'm playing at a high level," Falla said. "I'm confident in my game and myself."
Querrey added Los Angeles to crowns won earlier this year at Memphis, Belgrade and Queen's but was overpowered by Tipsarevic.
"Janko played great. He ripped the ball from both sides," Querrey said. "I was struggling to stay in any of the service games. He just played better than me. I was making errors all match but he was forcing me to go for tough shots."