The world number two was unbeaten in 20 games in the desert, which included winning the last three titles, going back to 2013, but the Australian was too good for him in sweltering conditions.
It was the second successive win for Krygios over the Serb, following victory in their first-ever meeting in Acapulco a fortnight ago and he finally looks ready to make the most of his undeniable talent.
Kyrgios was on best behaviour in the last-16 clash and won it thanks to some monster serving. He sent down 14 aces, which included second serves close to 120mph, won 85 per cent of points on his first serve and faced no break points.
A solitary break of serve of his own in the opening game of the match was enough to help him win the first set and while Djokovic offered some brilliant tennis in response to take the second set to a tiebreak, the Australian raced to a 3-0 lead and did not look back.
He said on Sky Sports 1: "It feels good, I knew what I had to do today, it was always going to be tough, he is a great champion.
"It's just another match for me I have to get ready for tomorrow. I am serving really well, that is creating chances for me to put pressure on their service games. My mentality is improving and I am trying really hard to fight for every point and just compete."
Kyrgios, whose world ranking of 16 is on the rise, will face either Roger Federer or Rafael Nadal in the quarter-final.
He added: "Roger is one of my favourite players of all time, but I don't mind who I play, they are both great champions."
Djokovic's defeat strengthens Andy Murray's position at the top of the rankings, as the Serb drops a whopping 990 points compared to the 20 Murray loses for his second-round exit.