Hrbaty had only beaten Blake once before - back in 2005
Dominik Hrbaty upset James Blake 6-4 4-6 7-6 (7-1) to secure a surprise win for Slovakia over defending champions the United States in the Hopman Cup.
With Dominika Cibulkova having earlier beaten Meghann Shaughnessy 6-2 6-2, that gave Slovakia a decisive 2-0 lead.
The US must now bounce back in their matches against Australia and Germany if they are to make Friday's final.
Germany beat Australia in their first tie, despite Lleyton Hewitt winning on his return from a five-month lay-off.
The former world number one has not played since losing to Rafael Nadal at the Beijing Olympics.
He was sidelined by a chronic hip injury which required surgery but fought back from a set down to beat Nicholas Kiefer 6-7 (6-8) 6-3 6-2.
That levelled the tie at 1-1 after Sabine Lisicki's 4-6 6-2 7-5 win over Casey Dellacqua had given Germany an early lead.
It was to no avail, though, as Lisicki and Kiefer combined to beat Dellacqua and Hewitt in the deciding mixed doubles.
The German pair took the decisive tie-break 10-5 after the first two sets had been shared 6-7 (2-7) 6-3.
That leaves the US and Australia winless after one match each, with Slovakia and Germany leading the way in Group A.
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 in Group B, while France beat Taiwan on Saturday.