Slovakia's Hantuchova, who needed just 47 minutes to dispatch Paszek, set up a second-round clash with second-seeded Agnieszka Radwanska.
Defending champion Tamira Paszek was forced to retire with a left thigh injury from her first-round match against 2009 champion Caroline Wozniacki at Eastbourne on Tuesday.
Paes and Elena Vesnina overcame a stiff resistance from unseeded team of Pakistan's Aisam-Ul-Haq Qureshi and Sofia Arvidsson of Sweden in the first round.
Tennis Australia said on Monday it was confident players would not boycott the Australian Open over a pay disagreement, but it was taking the threat seriously.
Second-ranked Victoria Azarenka set up a Wimbledon semifinal against Serena Williams by beating unseeded Tamira Paszek of Austria 6-3, 7-6 (4) Saturday, despite failing twice to serve out the match.
Good thing Wimbledon schedules its middle Sunday as a day off. This year, that gave everyone a chance to catch their breath after an eventful Week 1. Really, when action resumes Monday with all 16 men's and women's fourth-round matches, what could Week 2 possibly have in store to equal what the first six days offered?
Four-time winner Serena Williams survived a major scare before battling into the last 16 at Wimbledon on Saturday, while defending champion Petra Kvitova took the express route into the second week.
Austria's Tamira Paszek saved two match points to send former world number one Caroline Wozniacki crashing out of Wimbledon under the Centre Court roof on Wednesday.
Tamira Paszek rallied from a set and a break down to overhaul world number eight Angelique Kerber 5-7, 6-3, 7-5 on Saturday in the final of the WTA Eastbourne tournament.