The hosts made light of the absence of women's world number one Naomi Osaka as Doi beat Richel Hogenkamp 6-3, 6-4 before Hibino thrashed Bibiane Schoofs 6-1, 6-2 in Osaka.
A nightmare first day leaves the Dutch on the brink of relegation to the Europe/Africa group one just three years after narrowly missing out on a place in the Fed Cup final.
"I tried to mix my shots up a bit more, use more slice and come to the net," said Hibino. "That's something I felt I needed to improve on and it worked today."
Doi exorcised her demons after squandering a match point in Japan's 3-2 first-round defeat by Spain in February, a result which left them staring relegation in the face.
"I was totally aware of avenging that loss," she said. "It was important to get that off my back and deliver a good win for Japan."
Japan's Fed Cup team returned to world group two for the first time in five years with victory in last year's playoffs and are desperate to avoid an immediate return to Asia/Oceania group one.
They will get three bites at the cherry on Sunday as they seek to survive the drop, in the doubles and two reverse singles.
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