The Czech faced the match points in the second-set tiebreak before finishing off the Belgian in 2 hours, 16 minutes at the Wimbledon warm-up tournament.
"I believed until the very last point was played. I was feeling quite good on the court even though the score didn't look like that," said Berdych, who won this tournament in 2007. "I know how tough it is to close the match, and I used my experience over him."
Berdych only broke Bemelmans' serve once, to open the third set, and sealed the match with an ace.
Berdych is the highest seeded player remaining after No. 1 Roger Federer withdrew on Monday -- but the 2010 Wimbledon finalist does not want to be called the favorite.
"That's just how the people and the media look at the tournament," he said. "For me, it's the same regardless of my seed. If I do well, I have a chance to win the tournament."
Monfils, ranked a career-high eighth this week, will next face Ivan Dodig of Croatia.
Tommy Haas of Germany, the 2009 Halle champion, was eliminated after losing to Andreas Seppi of Italy 6-2, 6-7(6), 6-3. Haas was playing in his second tournament after undergoing right hip and right elbow surgery last year.
"I played well at times. I was forcing it, wanting it too much," Haas said. "I just need to play matches. You can't practice getting to the second round of a tournament."
Sixth-seeded Florian Mayer had a harder time beating German compatriot Dustin Brown 7-6 (6), 2-6, 6-3. Mayer, who next plays Yen-Hsun Lu of Taiwan, came into the tournament with his highest ever ranking at No. 18. He is also his country's No. 1 but said that was of no significance.
"Of course I have more self-confidence, but that's because I'm No. 18 in the world, not because I'm No. 1 in Germany," Mayer said. "The most important thing for me is to move further up the world rankings.
Petzschner also reached the second round on Tuesday with a 6-2, 7-6 (5) win over another German, Dominik Meffert, and will next face Daniel Gimeno-Traver of Spain, who came back for a 1-6, 7-6 (5), 6-2 victory over Kazakhstan's Andrey Golubev.