The in-form German, who beat Roger Federer to win the ATP Halle tournament before Wimbledon, won 4-6 6-3 6-4 in just over two hours against the world number 12 and second seed.
Haas will face another local hope in the quarter-finals, after seventh seed Florian Mayer beat Robin Haase of the Netherlands 6-2 6-1.
Albert Ramos came through a tough match against the man who knocked Rafael Nadal out of Wimbledon, Lukas Rosol.
Rosol, who beat Viktor Troicki in the opening round of the German tournament, lost the opening set in a tie-break before winning the next, only for Ramos to come through a 7-6(8) 4-6 6-3 winner.
Fourth seed Marin Cilic of Croatia also progressed, beating Federico Delbonis of Argentina 6-3 6-2.
It was a bad day for the seeds in Switzerland as Paul-Henri Mathieu dumped third seed Stanislas Wawrinka out of his home tournament at ATP Gstaad with a 7-6(3) 7-6(8) second-round win.
Russian fourth seed Mikhail Youzhny also went out, losing 4-6 6-2 6-4 to Brazil's Thomaz Bellucci.
Spain's Feliciano Lopez came through a hard-fought match against Jan Hajek to make it into the quarter-finals, where he will face Bellucci.
Fifth seed Lopez lost the opening set to the Czech before coming through to win 6-7(3) 6-1 6-4.
Ernests Gulbis of Latvia beat Benoit Paire of France 5-7 7-6(3) 6-4.
One first-round match was played on Wednesday, as seventh-seeded Colombian Santiago Giraldo beat Henri Laaksonen of Switzerland 6-2 6-2.
In Atlanta, crowd favourite and fourth seed Andy Roddick set up a mouthwatering quarter-final clash with fellow American Michael Russell with a 7-6(4) 6-3 win over Frenchman Nicolas Mahut.
Russell booked his place in the last eight with a 6-7(5) 6-4 6-4 upset of fifth seed Kevin Anderson of South Africa.
In the other quarter-final that was decided on Wednesday, Kei Nishikori will meet Go Soeda in an all-Japanese clash.
Nishikori downed Ricardas Bernakis of Lithunia 6-4 6-7 6-4 while eighth seed Soeda saw off Igor Kunitsyn of Russia 6-1 7-5.