The Czechs are one win from their third final in five years. The winner of the best-of-five series will play Serbia or Canada for the title in November.
Stepanek overcame a sluggish start in the first match, defeating Juan Monaco 7-6 (3), 6-3, 6-2. Berdych, ranked fifth, followed with a 6-4, 4-6, 6-3, 6-4 victory over Leonardo Mayer on the fast indoor hard court at O2 Arena.
Argentina was without star player Juan Martin del Potro, who skipped the Davis Cup this season.
Berdych and Stepanek have a 12-1 record in Davis Cup doubles and can wrap up the series Saturday against Carlos Berlocq and Horacio Zeballos.
"We are 2-0 up, that's what we wanted. Now, the most important thing is to get ready for the doubles," Berdych said.
Berdych looked relieved after he edged his 93rd-ranked opponent in more than three hours. He had to save a break point before converting his second match point when Mayer hit a forehand wide.
"I'm grateful for the result," he said. "The first two sets were not ideal from me."
Said Mayer: "I tried to attack as much as I could. He was better."
Stepanek was playing his first Davis Cup singles this year and just days after his second Grand Slam doubles title at the U.S. Open on Sunday.
"I was trying to be active," said Stepanek, who had 13 aces. "It was an important match for me. I faced a great opponent, but I wanted to use to my favor the surface and the fans."
Stepanek converted his first match point to improve to 5-2 against Monaco. Stepanek also beat Monaco to clinch the 2009 Davis Cup quarterfinal for the Czechs, also at home on a fast court in Ostrava.
"It's just coincidence," he said. "But I think I was the better player in those two matches."
Stepanek missed the first-round victory at Switzerland because of a neck operation and was able to play only doubles in the 3-1 quarterfinal win at Kazakhstan. He and Berdych played all five matches in last year's final in Prague and beat Spain 3-2.
In the first set, Stepanek was frustrated at the net by Monaco's passing shots. The Argentine took advantage of his first break point to go 3-1 up but allowed Stepanek to get back into the set with a double-fault on break point in the following game.
"He played so much better than me," Monaco said. "I had my chances in the first set but couldn't make it. He impressed me."