The British No.1, who reached his first ever championship match in Marrakesh last month, proved to have too much firepower for his youthful rival, who made his big breakthrough during the Australian Open Series in January.
De Minaur, watched by his mentor and doubles partner for the week Lleyton Hewitt, chased down every ball with enthusiasm, however he lacked the weaponry required to trade successfully with his higher ranked opponent.
The match was played almost exclusively on Edmund’s terms, and he overcame a second set wobble to seal his spot in the last sixteen. The No.3 seed will encounter either Joao Sousa or Pedro Sousa next.
Since reaching the final of the Sydney Open, De Minaur has struggled to obtain victories at ATP level. In fact, his 6-3 6-1 triumph over Gastao Elias on Monday was just his second win in the big league since January.
The teenager did not make a promising beginning against his latest opponent, though, and was soon trailing by a double-break. Edmund was content to swing freely and let his forehand do the talking – and he eased to the opener for the concession of just two games.
Matters got decidedly more serious for De Minaur when he committed a double-fault to slip 2-1 behind in the second set. He had limited time to mount a comeback, but to his credit, he found an avenue back into the match.
A drop in standards from Edmund coincided with a rare flurry of winners from his vocal rival. The 19-year-old managed to pull level at four apiece, however his hopes of a stirring fightback were soon quashed.
A focused and determined Edmund secured a vital break to move 6-5 in front after an entertaining net exchange. De Minaur was furious after conceding his serve for a fifth time, and he lashed his racket off the dusty clay-court in disgust.
His frustration was understandable, and his mood darkened further moments later. Edmund stepped up to the line and completed the formalities on serve to maintain his interest in the competition.