Evans, Britain's No. 1 men's player, won his first ATP title on Sunday at the Murray River Open, but he could not build upon that victory here, losing 4-6 6-4 4-6 5-7 to his compatriot.
Unseeded Norrie broke Evans' serve early in the first set and did not look back, securing the first frame in relatively straightforward fashion. The pair then traded holds throughout the second set until Evans secured a crucial break in the final game to level the match at one set apiece.
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The third set followed a similar pattern to the first, however, with 25-year-old Norrie breaking early and maintaining his composure to ultimately move into a 2-1 lead in the match.
The final frame was markedly more dramatic, with Evans achieving an early break as he surged into a 3-0 lead before Norrie restored parity. Evans then broke again, however, to lead 5-3 and serve for the set.
But Norrie responded positively again, this time with back-to-back breaks before serving out the set 7-5 to take the match after three hours and 28 minutes on court.
In the women's draw, Britain's No. 1 Johanna Konta was forced to retire from her first-round match against Kuja Juvan moments after securing the first set.
Thirteenth seed Konta dropped one service game in the opening frame but broke her Slovenian opponent twice en route to sealing the set 6-4.
But the Briton was struggling with her movement and lost the first two games of the second set without winning a point.
The injured Konta, 29, quickly made the decision to retire from the match, seeing Juvan progress to the second round via walkover.
British No. 2 Heather Watson had more joy than her compatriot, advancing with a 7-6 (4) 7-6 (3) victory over Kristyna Pliskova.
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