Evans received code and time violations in quick succession early in the second set as his frustration spilled over in the course of a 6-4, 4-6, 6-4, 7-5 first-round defeat.
It was particularly disappointing for the British number one who had come into the tournament fresh from his victory in the Murray River Open warm-up tournament at the weekend.
But conversely it was a dominant and disciplined performance from his opponent, who saved a set point and won four consecutive games to prevent Evans from forcing a decider.
Evans was the favourite to move into round two but it was Norrie who struck first with an early break which sustained him through a tight opening set to take the advantage.
Having been quietly warned for an audible expletive as the opener edged away, Evans was riled by a code violation being followed almost immediately by a time warning in the first game of the second.
Nevertheless Evans retained enough composure to eke out a marathon opening service game, and the tie looked to be swinging his way when Norrie netted a volley to enable the favourite to pull level at one set all.
The topsy-turvy nature of the tie continued as Norrie, who has a Scottish father and a Welsh mother, piled pressure back on the Evans serve, breaking to go 2-1 up and once again protecting his serve to regain the lead as Evans simmered on the baseline.
Evans stepped up in the fourth, breaking immediately for a 2-0 lead then again for 5-3 when Norrie missed with a forehand.
Serving to level the match, Evans missed a set point chance when he stabbed a cross-court forehand wide, and Norrie seized his chance when Evans uncharacteristically double-faulted on his third break point.
Filled with momentum, a quietly-focused Norrie levelled then broke Evans again before serving out to seal an impressive victory and book his place in round two.