Hrbaty, coming back from a serious elbow injury last season that saw his ranking slide to No. 250, gave Slovakia a winning edge after teammate Dominika Cibulkova beat Meghann Shaughnessy 6-2, 6-2 in the opening women's singles match.
Hrbaty and Cibulkova defeated Shaughnessy and Blake 6-4, 7-6 (4) in mixed doubles to complete a 3-0 win.
Blake, ranked 10th, went into the match with a 2-1 career edge against Hrbaty, including a win at the Beijing Olympics in August. But Hrbaty's sole previous victory over Blake came in the 2005 Hopman Cup in straight sets.
Earlier, Sabine Lisicki won her opening singles match and then joined German teammate Nicolas Kiefer to beat Australia in mixed doubles and clinch a 2-1 victory.
Lisicki defeated Casey Dellacqua, coming from a service break down in the deciding set to win 4-6, 6-2, 7-5 and give Germany a 1-0 lead. Lleyton Hewitt of Australia returned from a five-month injury layoff to beat Kiefer 6-7 (6), 6-3, 6-2 and level the match.
The German pair then beat Dellacqua and Hewitt 6-7 (2), 6-3 and 10-5 in the match tiebreaker to claim the deciding mixed doubles.
Former No. 1 Hewitt hasn't played since losing to Rafael Nadal at the Olympics. Hewitt was sidelined by a chronic hip injury after Beijing and later had surgery.
"It's great to be back,'' Hewitt said. "It feels good, the hip feels strong. I've done everything in my power to get as close to 100 percent for the Australian summer and it's a matter of just trying to come out here now and play a lot of matches.''
Hewitt said he had trouble early Monday getting his rhythm.
"He's (Kiefer) a great all-court player, and it was hard to get a read,'' Hewitt said. "It was a matter of me hanging in there and weathering the storm.''
Dellacqua, playing her first match since being sidelined last September by a shoulder injury, served for the match at 5-4 in the third but lost 12 of the last 13 points and had 33 unforced errors overall.
On Sunday, the brother and sister combination of Marat Safin and Dinara Safina won their singles matches to give Russia a 2-1 win over Italy. France, which beat Taiwan on Saturday, plays Italy on Tuesday while Australia takes on Slovakia.
The U.S., Australia, Germany and Slovakia are playing in Group A, while Russia, France, Italy and Taiwan are in Group B. The winners of each group play in the final on Friday.
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