In the first match, Ivan Ljubicic spoiled Andre Agassi's return to the competition with a 6-3 7-6 6-3 trouncing before Roddick rallied to overwhelm Ancic on the back of some huge serving, inventive play from the backcourt and a solid defence.
Watching Agassi's loss from the locker room did not put the world number three in a good frame of mind ahead of his contest, but he managed to regain his focus after a shaky first set.
"It's a very vulnerable feeling because it affects you, but it doesn't have a direct impact on how your match is supposed to go," said Roddick, who nailed 32 winners, including 10 aces, to remain undefeated in singles matches on home soil.
"I'm not going to lie, I was really tight in the first set. But I'm happy I was able to dig down and find a way through it.
"This is a big stepping stone for me."
Ljubicic dominated Agassi with his huge serve and big forehand and rarely allowed the American to break him down off his weaker backhand side.
"I played great. Everything went my way," Ljubicic said. It can't get any better than this."
Confident after reaching four ATP finals this year, the Croat immediately seized control of the first set by breaking Agassi to 2-0 when the American erred on a forehand.
Agassi broke back to 3-4 but Ljubicic broke the eight-times grand slam champion to 5-3 when he forced him into a forehand error and then won the set with a 130-mph ace.
Frustrated with his inability to get his backhand deep, Agassi frequently consulted with team captain Patrick McEnroe and his private coach Darren Cahill.
REGAINED CONFIDENCE
Agassi improved midway through the second set, playing a brilliant game by mixing in drop shots with hard baseline blows and breaking Ljubicic for a 4-2 lead.
However, Agassi could not maintain his momentum, failing to serve out at 5-3 when on set point he missed a forehand down the line.
Ljubicic regained his confidence to take it to a tiebreaker, where he ripped five winners including two aces to take it 7-0.
A clearly frustrated Agassi began to press in the third set and in the sixth game, he and McEnroe got into a loud argument with chair umpire Lars Graf when he over-ruled a line call on game point.
Agassi swore at the official, but couldn't get Graf to change his mind and he was then broken in the game to 2-4 when he double faulted.
Ljubicic won the contest when he boomed an ace down the middle.
Agassi was despondent after the loss.
"At the end of the day, you are there to help the team," he said. "I might be called on to do that again on Sunday. I sure hope to do better."
On Saturday, Ancic and Ljubicic will take on Bob and Mike Bryan in the doubles rubber before the reverse singles on Sunday.
The American brothers are the world's number two ranked doubles team and are undefeated in Davis Cup play.
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