British number one Norrie lost in three sets 6-4, 6-7, 6-3 to rising Spanish star Carlos Alcaraz.
No such luck for Evans who was also on the wrong end of a 7-6, 7-5 score to world number eight Andrey Rublev.
Alcaraz’s reward for beating Norrie is a match against Rafael Nadal, who had to save four match points against David Goffin.
The five-time champion served for the match at 5-4 in the second set and even held match point before the Belgium rallied to force a deciding set.
Nadal, making a welcome return to the tour after a six-week layoff through injury, eventually went on to win the match 6-3, 5-7, 7-6.
The Spaniard had double reason to celebrate after watching his beloved Real Madrid book their place in the Champions League Final after an extra-time aggregate victory over Manchester City on Wednesday.
Rublev will now face Greece’s Stefanos Tsitsipas who put out Bulgaria’s Grigor Dimitrov in straight sets.
Defending champion Alexander Zverev is through to the next round after his opponent Lorenzo Musetti had to withdraw with an injury.
Germany’s Zverev will now face Felix Auger Aliassime in the quarter-finals after the Canadian comfortably defeated Jannik Sinner of Italy 6-1,6-2.
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