The Bryan brothers cruised to a 6-3, 6-1, 6-3 doubles win on the indoor clay at Zatika Hall.
The U.S. is 1-34 when trailing 0-2 in a Davis Cup match. The team's only comeback was against Australia in 1934.
It was the third time the second-ranked Bryans have taken the court in doubles with the U.S. Davis Cup team trailing 0-2. In the 2004 Davis Cup final in Spain and the 2006 semifinals at Russia, the twins kept the series alive by winning. The U.S. went on to lose both best-of-five series.
"Tomorrow, we hope to make history," Mike Bryan said.
Blake lost the opener to Karlovic, and Cilic beat Fish on Friday. Both matches lasted five sets and took a combined time of more than eight hours.
"Those were two very close matches," U.S. captain Patrick McEnroe said. "We certainly think we can win both matches, but first James has to beat Cilic. He thinks he has the game for Cilic."
Cilic, ranked No. 15 in the world, hopes to end the series before the fifth match.
"We now have a psychological advantage," Cilic said. "If you give Blake the initiative, he's most dangerous but if you put him on defensive, that's where my chances are."
With the victory on Saturday, the Bryans extended their Davis Cup record to 16 victories in 18 matches -- the best ever for an American doubles pair.
They needed a little more than an hour to cruise to a convincing win against Karanusic and Zovko. The Croatians made a last-minute change in their doubles pair, replacing big-serving Karlovic with Karanusic.
"It was obvious they tried to save their singles player for tomorrow," Bob Bryan said. "It made our job easier."
At one point, the Bryan pair won nine straight games, breaking the Croats four times.
The 32-time champion Americans have lost to Croatia the two previous times they met in Davis Cup -- in 2003 and 2005, when Croatia won the competition.
The U.S., which won two years ago, is bidding to reach the semifinals for the fourth straight year. The winner will face the Czech Republic or Argentina in the semifinals in September.