Berdych, an Australian Open semifinalist, dominated throughout as he cruised to a 6-3, 6-3, 6-0 victory for the defending champions in the first round matchup.
Never facing a break point, the seventh-ranked Berdych broke Sijsling early in each set and secured one break in the first set, two in the second and three in the third before converting his first match point with a powerful forehand winner.
"I tried to go on attack," Berdych said. "I'm glad that I got rid of the fatigue (from the Australian Open). I felt really good on the court and played accordingly."
The 46th-ranked Haase won the hard fought contest 3-6, 6-4, 6-7 (4), 6-2, 6-1 in 3 hours and 39 minutes on an indoor hard court at CEZ Arena.
Berdych and Stepanek are expected to team up for Saturday's doubles, and could face Thiemo de Bakker and Jean-Julien Rojer.
Haase broke Stepanek for a 3-1 lead in the final set and did the same in the sixth game before serving out, converting his first match-point with a forehand winner.
"I felt good," Haase said. "He had many break points but in the end I always played good. I served well and played some unbelievable points. Maybe I was a little bit more lucky in that today but I'm happy, of course."
Stepanek took advantage of only three of his 18 break-point opportunities while Haase posted 14 aces and hit 62 winners to Stepanek's 43.
The winner of the best-of-five series will face either Canada or Japan in the quarterfinals in April.
The 50th-ranked Stepanek took the first set after securing break points in the seventh and ninth games but allowed his 46th-ranked opponent to come back in the second set.
Haase broke him in the ninth game with a precise passing forehand down the line.
In the third set, Stepanek wasted four break points in the eighth game that would have had him serving for the set with a 5-3 lead. He also failed to convert three set points in the 12th game before prevailing in the tiebreak with his typical attacking play.
However, Haase fought back again in the fourth, racing into a 3-0 lead before converting his second set point and then going on to seal the final set.