This time, back on home court, Venus and Klaasen, the second seeds, lived up to their billing by grafting hard to put away fellow Kiwi Artem Sitak and Dutch partner Wesley Koolhof.
Venus and Klaasen were broken in the first game but rebounded immediately to claim the first set in 24 minutes. From there, it was anything but straightforward, though.
Sitak and Koolhof fought back to push out to a 4-1 lead in the second set. Venus and Klaasen battled back to level, only to concede, but then clintched the super tie breaker to prevail 6-1 6-7 10-7.
After losing to Sitak in the first round of doubles at the Classic last year, Venus was pleased to make amends.
"Any time you're at home you want to play well," Venus said. "One of us was going to be disappointed tonight and that was me last year so I'm excited to get the win with Raven and start our partnership off like this."
Venus and Klaasen progress to meet Poland's Marcin Matkowski and Pakistan's Aisam-Ul-Haq Qureshi, the defending champions who needed two hours to down Indian pairing Leander Paes and Purav Raja 6-7 (4) 7-6 (8) 10-7.