World number six de Minaur produced a clinical display on a sunny Andy Murray Arena to win 6-4 6-1 in little more than an hour - improving his record over Shapovalov to 6-0.
De Minaur stepped up a level from the previous day when he beat another Canadian, Gabriel Diallo, looking every bit the accomplished grass-court player that he is.
Next up is Nakashima, who eased to a 6-2 6-2 victory over Peru's Ignacio Buse.
British wildcard Arthur Fery also reached the quarter-finals as he beat wily French veteran Adrian Mannarino 7-6(7) 6-4.