The strategy worked as he applied pressure and broke de Minaur at 1-1, but with Kecmanovic serving for the set at 3-2, the Sydneysider ripped a forehand winner to level at 3-3.
De Minaur rode that momentum and dominated the tiebreaker for a commanding 2-0 advantage.
Kecmanovic stuck to his tactics and was finally rewarded in the third set when he broke de Minaur at 2-1 and closed out the set.
However, the Australian showed great composure to recover from that setback and produced some outstanding tennis in the fourth set, where he dropped just five points to seal the win in just under an hour-and-a-half.
“This is what you expect in these conditions,” de Minaur said.
“A match can turn quickly. I didn’t play badly, [but] he just played well in the important moments.
“I just had to regroup and stick to my game.”
Rudd beat Fokina in a hard-fought five-setter to move to join Kecmanovic at 1-1 in group A.
“Casper played a hell of a match today and it’s going to be incredibly tough, but this is what we’re here for,” de Minaur said.
“Everyone is playing at a high level, so I have to be ready for it.”