As Sakkari's confidence grew, so did Collins' unforced error count and the Greek player battled to set points at 5-4.
A chaotic second set produced eight breaks of serve, but Sakkari held throughout the tie-break to secure passage to the last four.
Ahead of learning the identity of her opponent, former world number two Kuznetsova said: "I'll see whoever wins that match and just prepare my tactics".
Williams won this event in 2000 and 2002, earning her eighth appearance in the decider as recently as 2016.
Former world number one Azarenka, a two-time Australian Open victor, had won the first set 7-6 (7-4) but was trailing 0-3 in the second when she withdrew.
Venus' defeat follows the shocking upset three days ago of her sister Serena, who suffered the most lopsided loss of her career, 6-1, 6-0 to Johanna Konta in round one.
In a rematch of the pair's Hobart International final in January, Buzarnescu stepped up a gear in the second set, and reeled off six games in a row in the third to take a 4-6 6-3 6-1 victory.
"They're two very different players, and both of them are going to be really hard opponents for the final, but I'm just looking forward to playing".
Svetlana Kuznetsova had taken the first set against Yulia Putintseva and Donna Vekic was leading Magda Linette 3-0 in the opening set of their encounter when rain interrupted play. The Romanian will face No. 4 seed Elise Mertens.
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