It's a good draw for Venus and Klaasen who are seeded to meet the 8th seeds Nikola Mektic of Croatia and Austria's Alexander Peya in the third round.
The other Kiwi in the tournament Artem Sitak and his Dutch partner Wesley Koolhof have avoided seeded opponents in the first round.
They have been pitted against Germany's Andre Begemann and Croatian Antonio Sancic who are also doubles specialists.
Sitak knows the pair well but says "it's a pretty good draw, could have been worse."
"I played with Begemann for five tournaments two years ago and I have played against both him and Sancic separately before. They are not seeded but they made the final in Houston this year so we have to take the match very seriously," Sitak said.
Sitak and Koolhof could face the 9th seeds Ivan Dodig of Croatia and American Rajeev Ram if they win their first round match which is likely to be played in a couple of days time.
Meanwhile Erin Routliffe has won her first round qualifying match at the ITF tournament in Hua Hin Thailand. The 23 year old has beaten Australian Alana Parnaby 7-5 6-2.
Routliffe will next face Thailand's Tamachan Momkoonthod.
The Kiwi and her Mexican partner Victoria Rodriguez are the top seeds in the doubles.
They face a Serbian and Slovakian pair in the first round.