Edmund beat Murray at Eastbourne in June – in the third match of his return during the grass-court season – before the world number 832
Edmund, 23, said: “I gave my best of what I had on the day, it just didn’t work out. It would have been nice to hold serve and maybe even control what I can and take [the third set] to a tie-break but it didn’t happen.”
Defending champion and world number three beat Tunisia’s Malek Jaziri 6-2 6-1 and will play his brother in the third round.
After five years together on the ATP Tour, this will be their first meeting on court. “It’s going to be very interesting for me. It will be a special day,” said Alex Zverev. “Not many families can say they have two players playing at this level.”
Belgian third seed survived a scare against France’s Pierre-Hugues Herbert to win 6-2 1-6 7-6 (7-5) while Japan’s beat American qualifier Donald Young for the second year in a row, winning 6-3 6-4.
He will face Canadian in the next round, while Goffin plays American Fifth seed withdrew from the tournament with a hip injury, having retired during his Atlanta Open quarter-final last week.
Elsewhere, British number two is through to the quarter-finals of the Los Cabos Open in Mexico, following a 6-3 6-3 victory over Spanish eighth seed Feliciano Lopez. Norrie, 22, will play Frenchman in the last eight.