Shibahara and Aoyama powered through the opening set 6-3, breaking twice for a quick 3-0 lead. Cross and Marino hit back in the second, edging it 7-5 to level the match, before the Japanese pair regained control to dominate the decider.
"I was very nervous before the match. I just tried to focus my energy on the court and I'm happy with today’s win," the 37-year-old Aoyama said.
"I’m really happy that I got the doubles done today," an emotional Shibahara added, having lost her singles tie.
Canada's 18-year-old Victoria Mboko edged Japan's Shibahara 6-4, 6-7(8), 7-5 in a marathon opening clash. Mboko fired eight aces to take the opening set after racing to a 2-0 lead. In the second, Shibahara fought back, saving three match points in the tiebreak before levelling the contest.
Mboko trailed early in the decider but recovered to break for 4-4, and after squandering three more match points, sealed victory with a forehand winner on her seventh.
Japanese number one Moyuka Uchijima breezed past Marina Stakusic 6-3 6-3 in one hour and 15 minutes to level 1-1 and force the doubles decider.
Uchijima, ranked 77 places higher, won 13 straight points to take the opening set in a little over 30 minutes with a delicate dropshot. After Stakusic saved two break points at the start of the second, Uchijima pounced for a 4-2 lead and sealed victory to rapturous home support.
Having played the qualifiers without injured Naomi Osaka, Group A leaders Japan join hosts China, defending champions Italy, and fellow qualifiers Ukraine, Spain, Britain and Kazakhstan for September’s eight-team finals in Shenzhen.
The final spot will go to either Slovakia or the United States in Group C. They face off in Bratislava later on Sunday.