Haas, who has steadily climbed up the world rankings this year to No. 36, broke Mayer three times in the hard-court match and won 83 percent of his first-serve points.
Haas advanced to the quarterfinals, where he will face fellow German Tobias Kamke.
Kamke moved on by ousting Australian 6-4, 6-3.
Alexander Dolgopolov of Ukraine, the second seed in the tournament, cruised past Ruben Ramirez of Spain 6-1, 6-3 and will face U.S. veteran James Blake in the quarters.
Blake, who won the Citi in 2002 and was runner-up in 2005, knocked off Swiss qualifier Marco Chiudinelli 6-2, 6-4 Wednesday.