The 20-year-old Davis started 2014 ranked No. 72, and has moved up to No. 55.
Davis reached the Indian Wells fourth round, but withdrew from the match with a stomach virus.
"I'm playing really well and I have a lot of confidence," Davis said. "I think there's a time for everything and I feel like this is my time."
From 1-1 in the first set, Davis jumped ahead to a 4-1 lead. In the second set, Zhang started with a 3-1 lead, but Davis won the next five games to take the match.
Following the U.S. Open, Davis switched from working out of the Chris Evert Academy to the USTA Player Development program.
"Switching to the USTA has honestly been a great plus," Davis said. "Just hitting with other girls and making friends, and not everything there is about me.
"It's caused me to be more independent and I'm looking out for myself now."
Fellow American Christina McHale, who is one of the other Americans training at the USTA Center in Boca Raton, defeated Zheng Jie of China 6-4, 6-2.
Wildcard recipient Victoria Duval didn't fare as well as her fellow Americans, losing to qualifier Kiki Bertens 7-6 (5), 6-1.
Del Potro has been troubled by his left wrist since winning the Sydney title at the beginning of the year. At the recent Indian Wells tournament he played one doubles match, but then withdrew from the singles.
The 37th-ranked Andrea Petkovic of Germany, a top 10 player back in 2011, posted a 6-3, 6-4 win over Maria-Teresa Torro-Flor of Spain.