Venus was thrilled with the performance.
"The conditions were better, not quite as windy and we had a really good first serve percentage so that set us up well at the net and took care of our service games. We both returned well and were aggressive and it worked today." Venus said.
Venus and Puetz will now meet Australian wildcard pairing Jason Kubler and Christopher O'Connell in the third round.
Fellow Kiwi Marcus Daniell failed to advance, with he and doubles partner Frederik Nielsen unable to upset the No 2 seeds in the men's doubles draw, going down to Joe Salisbury and Rajeev Ram 6-1, 6-2.
Daniell and Nielsen were under pressure for the majority of the match, with Ram and Salisbury comfortable behind their own serve and aggressive against that of the opposition.
The No 2 seeds forced seven break points throughout the match, converting on four of them, while Daniell and Nielsen did not put themselves in position to break serve once.
Ram and Salisbury hit a total of 21 winners in the match to 11 by Daniell and Nielsen; the latter hitting more unforced errors than winners with 13.
Another seed ousted by Cornet
Tour veteran Alize Cornet is developing a reputation as a seed destroyer at the Australian Open. After eliminating No 3 seed Garbiñe Muguruza in the second round, France's Cornet held her nerve for a comeback win against No 29 Tamara Zidanšek.
In a match where both players struggled mightily to hold serve, it was Zidansek who got the better of the first set to take it 6-4.
Things looked awful for Cornet through the early stages of the second set as he fell behind 4-1 - dropping two of her first three service games. However, Cornet went on a run of winning seven games in a row, winning the second set 6-4 and taking a 2-0 lead in the decider.
Zidansek tried to get back into the set, but struggling to win games on serve and a myriad of unforced errors saw her fall 6-2 and exit the tournament.
Zidansek had more break point opportunities than Cornet in the match (16 to 15), however Cornet converted more (8 to 6). The tale was told in the statistics as Zidansek hit 35 winners, but also a whopping 63 unforced errors. Cornet only hit 16 winners, but her 39 unforced errors paled in comparison to that of her counterpart.
Cornet will now meet 14th seed Simona Halep in the fourth round, after Halep decimated Danka Kovinic in straight sets.