The Masters 1000 tournament lost its headline act on Sunday after world number one and top seed Rafael Nadal withdrew in a bid to stay healthy following his Rogers Cup success.
Edmund, meanwhile, earned his first Cincinnati victory by defeating McDonald 6-3 6-2 thanks to 10 aces and just one point dropped on his serve.
Next up for Edmund is either Frances Tiafoe or Denis Shapovalov.
Frenchman Adrian Mannarino saved a match point in his 6-7 (7-9) 6-2 7-6 (9-7) victory over Marco Cecchinato.
Mannarino had trailed 6-5 in the third-set tie-break before rallying to book his spot in the next round.
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