The 43-year-old Williams, a seven-time Grand Slam champion, dropped to 2-4 in six career matches against the 28-year-old Keys.
The 16th-ranked Keys broke Williams twice in the first set. She recorded two more breaks in the second and held on for the win.
Pliskova, ranked No. 23 in the world, had 11 aces and seven double-faults. She converted five of 16 break points.
Zhu had two aces and eight double-faults. She broke on two of her three opportunities.
As the second set began, Boulter continued to assert her dominance, breaking Marino's serve and building a 3-0 lead. She clinched the straight-sets victory in 65 minutes.
Boulter had an impressive performance at the Rothesay Open in June, earning her first career WTA singles title. Next up is a match against Coco Gauff.