Federer routed Mischa Zverev 6-0, 6-0 in a very efficient 39 minutes. In a dominant performance, Federer lost only eight points in six games serving and took two-thirds of the points off Zverev's serve.
Overall, Federer won 71 percent of the points in each set.
Haas, the No. 3 seed, was on the court nearly 2 hours in a 6-7 (4-7), 6-3, 6-3 victory over Gael Monfils. Monfils had 14 aces but Haas ended up with the better serving statistics, facing only one break point and winning 75 percent of the points on serve to 66 percent for Monfils.
While they'll play in Saturday's semifinals this year, Haas defeated Federer in the 2012 Gerry Weber Open final. However, he is just 3-10 versus Federer all-time. The first two wins by Haas in the series were in 2000 and 2002.
Second-seeded Richard Gasquet stopped No. 8 Florian Mayer 6-3, 7-6 (7-4) in a match that featured just one break. Mikhail Youzhny, who also didn't lose his serve Friday, eliminated sixth-seeded Philipp Kohlschreiber 6-3, 6-2.
Gasquet and Youzhny have split their previous eight meetings, with Gasquet taking a straight-set win earlier this year in Miami.