The seventh seed plays a remarkable number of three-setters and a second-set lapse cost her again here, although she recovered well in the decider to defeat Doi 6-2 3-6 6-1.
Kvitova, the 2011 Wimbledon champion, has been consistent only in her inconsistency this season and today's win was a fifth three-setter out of her last six victories.
The Czech next meets Serbian Bojana Jovanovski, who put out Germany's Andrea Petkovic 6-2 6-4.
Ana Ivanovic was the first winner of the day, the 13th seed thrashing Anna Tatishvili 6-2 6-0 in just 58 minutes.
Ivanovic split from British coach Nigel Sears after Wimbledon and is now working with Serbian pair Nemanja Kontic and Zlatko Novkovic and Sven Groeneveld through her sponsors, adidas.
The former world number one had enjoyed good preparation for the US Open until a first-round defeat by Alize Cornet in Cincinnati.
Ivanovic said: "I've been playing really well and I had a few tough losses. It's obviously hard, more so emotionally than anything else. I'm very confident with my game.
"I know I did a very good preparation. I have a new team with me. Obviously it takes time to get comfortable, to get things to work smoothly. I'm very happy at the way everything is."
There were also comfortable wins for Maria Kirilenko and Roberta Vinci.