The 29-year-old Pole on Wednesday saw off the 89th-ranked American 6-1, 6-4, 6-3 in the second round of the men's singles at the grass-court Grand Slam tournament.
Majchrzak, who is ranked world No. 109 by the Association of Tennis Professionals (ATP), will next face France's Arthur Rinderknech for a place in the round of 16.
Meanwhile, Poland’s Iga Świątek has progressed to the second round of the women's singles at Wimbledon with a 7-5, 6-1 win on Tuesday over Russian Polina Kudermetova.
Świątek, who is ranked world No. 4 by the Women's Tennis Association (WTA), will take on American Caty McNally on Thursday for a place in the last 32.
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Source: IAR, PAP