Murray was the architect of Britain's Davis Cup title triumph in 2015 but injury ruled him out of the trip to Marbella to face Spain, playing in their clay court comfort zone.
But world 114 Norrie, making his debut in the competition, stunned Spain's 23rd-ranked Roberto Bautista Agut 4-6, 3-6, 6-3, 6-2, 6-2 to pull Britain level at 1-1 in the World Group tie after world number 21 Albert Ramos-Vinolas had seen off Liam Broady 6-3, 6-4, 7-6 (8/6).
Spain, the five-time Davis Cup winners, were expected to cruise through the tie even without injured world number one Rafael Nadal.
But 22-year-old Corrie, who had never before competed on European red clay, was undaunted by facing a player who had not lost a Davis Cup match since 2014.
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"It is 100 per cent the best day of my career," said Corrie. "I backed myself physically and mentally against the guy. I wanted to work him as hard as I could."
"He played unbelievable," the former two-time French Open champion told daviscup.com.
Defending champions France were also level with the Netherlands in Albertville, but only after a shock in the first rubber when world number 369 Thiemo de Bakker downed the 25h-ranked Adrian Mannarino 7-6 (7/4), 6-3, 6-3.
Mannarino was a late call-up after first choices Jo- Wilfried Tsonga and Lucas Pouille pulled out injured.
"I don't fear the French. I have beaten them before and I knew that I had the weapons to defeat them again," said De Bakker.
In Brisbane, Australia and Germany were also 1-1 but world number five Alexander Zverev survived a huge scare before seeing off the 139th-ranked Alex de Minaur 7-5, 4-6, 4 -6, 6-3, 7-6 (7/4).
Nick Kyrgios pulled the hosts level seeing off Jan- Lennard Struff 6-4, 6-4, 6-4 on the back of 21 aces.
Croatia, missing Australian Open runner-up and world number three Marin Cilic, are 1-1 at home to Canada in Osijek.
Borna Coric claimed a 3-6, 6-2, 6-3, 6-2 victory over 85th-ranked Vasek Pospisil before fellow 'NextGen' star Dennis Shapovalov, ranked 48 eased to a 6-4, 6-4, 6-2 win over Viktor Galovic, the world 181.
Japan, without talisman Kei Nishikori, are 1-1 with Italy in Morioka.
Fabio Fognini, the world 22, saw off 100-ranked Taro Daniel 6-4, 3-6, 4-6, 6-3, 6-2 before Yuichi Sugita levelled by beating Andreas Seppi 4-6, 6-2, 6-4, 4-6, 7-6 (7/1).
Elsewhere Friday, Belgium, the 2017 runners-up, opened a 2-0 lead over Hungary who are bidding to reach the quarter- finals for the first time.
In Astana, Kazakhstan are also 2-0 to the good against 2014 champions Switzerland who are without Roger Federer and Stan Wawrinka.
John Isner made it 2-0 by seeing off Dusan Lajovic 4-6, 7-6 (9/7), 3-6, 6-3, 7-6 (7/4).