The world number 103 pulled off one of the biggest Wimbledon shocks when he beat Rafael Nadal in the second round last month and showed it was no one-off as he eased beat Haase 6-4 7-5.
The 26-year-old Czech will meet local hopeful Bjorn Phau in the next round after he beat Martin Fischer 6-3 6-3.
Seventh seed Lukas Kubot also crashed out after he lost to 21-year-old local hopeful Cedrik-Marcel Stebe 6-2 0-6 6-3.
Veteran German Tommy Haas was the only seed to progress as he rallied past Igor Andreev 4-6 6-2 6-2.
Thomaz Bellucci will meet Australian third seed Bernard Tomic in the second round by beating Robin Kern 7-6 (7/3) 6-2.
French duo Benoit Paire and Jeremy Chardy were joined in the next round by Sergiy Stakhovsky and Tobias Kamke.