The Kiwi and South African combination are eyeing a deep run at Flushing Meadows which should just about secure them a place at the ATP World Tour finals in London. They are currently 6th in the race with the top eight teams after the Paris Masters in early November qualifying for the lucrative tournament at the O2 Arena.
Their form over the past couple of months has made them one of the most feared doubles teams on tour having reached the Wimbledon final in July and the ATP Masters 1000 final in Toronto earlier this month.
Venus and Klaasen will face either Argentine Maximo Gonzalez and Chilean Nicolas Jarry or Spaniard David Marrero and Poland's Marcin Matkowski in the second round.
Daniell and Koolhof started well taking the first set comfortably but had to dig deep in the second set against an experienced pair.
Daniell had to save two second set points on his serve at 5-6 to take it into a tie breaker which was a roller coaster affair. Daniell and Koolhof shot out to 3-1 and trailed 5-3 before saving two set points at 6-4. They converted on their second match point, winning the tie breaker 10-8.
They will face either in form fourth seeds Bruno Soares and Jamie Murray or Guido Pella and Albert Ramos Vinolas in the second round.
The third Kiwi in the field Artem Sitak and his Indian partner Divij Sharan will face the American wildcard pair of Martin Redlicki and Evan Zhu on Friday morning NZT.