The seventh seed, who beat Dinara Safina to win the title in 2008 and has returned to her best form after a slump, was outplayed initially by Doi but recovered to win 3-6 6-3 6-4 with the clock past 9pm local time.
She was on tenterhooks until the end though and failed to serve out the match at 5-2 in the decider, showing her frustration as she blazed a forehand wide.
Doi then held serve with a crafty drop shot but Ivanovic kept her nerve, moving 40-0 ahead on serve and sealing victory when Doi fired a backhand long. Ivanovic will face Croatian teenager Donna Vekic in the third round.