Norris overcame a woeful start which saw him hand over the lead from pole within seconds, before going on to pass the championship leader on Lap 18.
From there, he never looked back, delivering a flawless drive to finish more than 22 seconds ahead of the chasing pack, and in turn, narrow the gap at the top of the drivers' standings to 70 points.
Reflecting on his triumph post-race, the 24-year-old admitted he was taken aback by how easy it was to close the gap on Verstappen in the early stages, and then open up a sizeable advantage of his own after retaking the lead.
"Saturday is always a good indication of what you are able to do and we were very quick yesterday so we had high hopes," he said. "The car has been lovely to drive.
"I thought Max would be quicker than he was. It seemed like he was the outlier as he dropped all the way back to the Ferraris, which was a surprise."
Pressed further on whether he was now in a title fight with the Dutchman, Norris insisted that he has always had the Red Bull in his sights.
"I have been all year, it's not like I have decided just do it now! I have had the car for a while, that is obvious. It has been phenomenal.
"I wouldn't say we have been the best since Miami but on average we have been. We had opportunities to beat Max and haven't. But that is in the past.
"We have tried to improve in lots of areas and a result like today proves that. It feels like a good start to the second half of the year."