Safin won the men's singles before the Czech pair got a consolation point when Novak and Strycova combined for a 3-6, 7-6 (1), 11-9 win the mixed doubles.
Safin, who spiraled down to No. 77 in the ATP entry system rankings due to a chronic wrist -problem in 2003, said he'd surprised himself with his early season singles form.
"It was tough, I was not scared because I was playing really well and this match was a very important match for me," said the 2000 US Open champion.
"The second match of the year, I am feeling great and fighting and running and doing everything as well to beat him."
Safin beat Frenchman Fabrice Santoro 6-3, 6-3 in his opening singles match here, his first singles win in nine months.
The Russians face the defending champion US on Friday and must beat Lindsay Davenport and James Blake 3-0 to have any chance of reaching the final.
Safin said he'd had felt twinges in his wrist, but nothing serious enough to sideline him.
"Yesterday I had some problems with the wrist, but it went away and didn't really bother me today," he said.
In matches later Thursday, Australia was against the Slovak Republic and Hungary faced Canada. Belgium had to forfeit its scheduled match against Hungary after Kim Clijsters withdrew from the tournament with an ankle problem.
AAPT Championships
Teenage wild card Todd Reid followed his first-round upset of top-seeded Wayne Ferreira with a 6-3, 6-2 win yesterday over Dutchman Raemon Sluiter to advance to the quarterfinals of the AAPT Championships.
The 19-year-old Australian next faces sixth-seeded Jarkko Nieminen of Finland, who had a 7-6 (2), 6-4 second-round win over Italian Davide Sanguinetti.
Big-serving Greg Rusedski's comeback after four months off with back problems ended in the second round, when he lost 6-2, 6-2 to Frenchman Cyril Saulnier.
Rusedski last played in September for Britain in the Davis Cup and his only other match at Memorial Drive in Adelaide was a rain-interrupted 6-4, 6-1 win over Swiss qualifier Stanislas Wawrinka in the first round.
Seventh-seeded Alberto Martin of Spain was against Dominic Hrbaty later yesterday before former No.1 Patrick Rafter, a dual US Open champion and two-time Wimbledon finalist, made his competitive comeback in men's doubles.
Rafter, who last played in November, 2001, was to partner fellow Australian Josh Eagle in men's doubles against Vincent Spadea and Mark Merklein.
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