Tsonga was making his debut in the clay-court event and had a bye into the second round. But he has never won a title on clay and was outplayed by the 134th-ranked German, who once was ranked No. 2. Tsonga is ranked fifth, but never had a break point against Haas.
Third-seeded Marin Cilic cruised past Matthias Bachinger 6-3, 6-2 to reach the last eight.
Eighth-seeded Marcos Baghdatis of Cyprus rallied to beat German qualifier Dustin Brown 1-6, 6-4, 6-1.
In Budapest, top-seeded Sara Errani of Italy reached the Budapest Grand Prix quarterfinals for a second straight year after overcoming Hungarian qualifier Melinda Czink 6-4, 1-6, 6-1 yesterday.
She'll play Alberta Brianti, who defeated Lesia Tsurenko of the Ukraine 5-7, 7-5, 6-4. Elena Vesnina of Russia ousted second-seeded Ksenia Pervak of Kazakhstan 6-2, 6-3.
“I tried to be creative and served a good percentage,” Vesnina said.
Fourth-seeded Klara Zakopalova lost, 6-3, 6-3 to Barbora Zahlavova Strycova, who will take on Marina Erakovic for a place in the semifinals.
Sixth-seeded Petra Martic beat Su-Wei Hsieh 6-4, 6-1, and meets Vesnina next. The other quarterfinal will feature Aleksandra Wozniak against Anna Tatishvili.
In Oeiras, Portugal, Stanislas Wawrinka recovered from a shaky start to beat Spanish qualifier Ivan Navarro 7-6 (5), 6-1 yesterday and move into the quarterfinals of the Estoril Open.
The big-serving Swiss saved break points in his first two service games before being broken in the sixth game on a double-fault. He broke back immediately and had five set points at one stage in the tiebreaker.
The third-seeded Wawrinka overpowered his opponent in the 20-minute second set, serving out the match in damp and windy conditions at the rain-disrupted clay event.
In the women's event, top-seeded Roberta Vinci advanced to the quarterfinals with a 6-2, 6-0 victory over Maria Joao Koheler of Portugal.