The 22-year-old was ruthless in his destruction of the South American, who arrived on Court 6 buoyed by his upset of Frenchman Jo-Wilfried Tsonga in the first round.
Edmund broke his opponent seven times through a tick over two hours of first-strike tennis to seal a third round clash with the imposing South African Kevin Anderson.
Olivo called the trainer while staring at a double break deficit in the third set but the Brit was relentless, forcing an errant forehand from the Argentine at match point to seal his progression.
“That’s what it’s like in sport, you have to be ruthless, keep pushing the guy down because that’s the reality, he would do the same to you,” Edmund said courtside.
“He’s a guy that just keeps going and I knew that so I just had to keep beating him basically.”
Certainly, Olivo squared off against the 22-year-old bubbling with confidence following his round one victory and the opening set was a cagey affair.
The pair traded breaks to open the encounter and Edmund’s serve that had bode so well during his first round win over Gastao Elias was looking uncharacteristically shaky.
But he steadied himself and the set stayed on serve until the eighth game when Olivo double faulted to gift the 22-year-old a vital break of serve.
It would be in the vain, however, as the South American displayed the fighting spirit that characterized his momentous win over Tsonga, outlasting Edmund in a pulsating forehand rally to recover the break.
The set appeared to heading to a tie-break until the Brit summoned energy at deuce in the twelfth game.
Olivo saved one set point with a supreme passing shot when cornered on the deuce court but was hapless when he sent a running crosscourt forehand long that sealed the opening set for his British counterpart.
52 minutes had ticked over when Edmund began the second set and it was the 22-year-old’s burst of acceleration that fashioned break point at 2-1.
He burst forward to retrieve a hanging dropshot from Olivo and generated enough power to force his opponent into a defensive lob that was easily put away with an overhead to confirm the break.
Edmund consolidated the break with a hold to 15 and served out set two in emphatic fashion as the South American’s hopes of producing another upset appeared to be diminishing.
And his body let him down in the decisive third set, only just squeezing through a five-minute service game to hold for 1-0.
The break came at a similar juncture to the previous set; this time Olivo caught the tip of the net with a running forehand as he scampered to retrieve one of Edmund’s many rasping groundstrokes.
The double break arrived soon after and when he informed the umpire of his desire for a medical time out the writing was on the wall.
Two hours and two minutes had barely elapsed when the Argentine arrowed a forehand long on match point.