Murray had 47 of the 99 unforced errors during the nearly three-hour match in the heat of the Southern California desert.
Federer held on through two tiebreakers to beat Tursunov in what was not a dominant performance from the former world No. 1 and 17-time Grand Slam champion.
However, the match did showcase the confidence he has regained with a strong start to this year after a disappointing — by his standards — campaign last year.
“Now I feel like I’m in a good place. Zen on the court,” Federer said. “I know what my solid level is. Even if I won six and six today, I just feel like I was calm and served for the set — OK, got broken, still managed to stay calm.”
Federer broke Tursunov to open the match, but was broken as he served for the set at 5-4 before winning the tiebreaker. He recovered an early break in the second set before dominating in the second set.
Federer arrived in California on the heels of a victory in Dubai, where he beat Serb Novak Djokovic in the semi-finals and Tomas Berdych of the Czech Republic in the final.
That win was his first title in nine months and backed up a solid semi-final showing at the Australian Open, where he posted wins over the UK’s Andy Murray and Frenchman Jo-Wilfried Tsonga.
“It’s just good to beat top-10 players from time to time,” he said.
In the women’s singles, top seed Li Na downed Karolina Pliskova of the Czech Republic 6-3, 6-4, while the US’ Sloane Stephens beat 11th-seeded Ana Ivanovic 7-6 (3), 6-4.