Norrie, who won the Indian Wells title in 2021, will play Australian world number six Alex de Minaur in the last 32.
“I have been having an amazing preparation,” said Norrie.
“I got here with time – a lot of time – so I’ve been practising really really well against all types of players, and the weather’s been unreal, so good vibes all around.”
World number one Carlos Alcaraz was a 6-2 6-3 winner against Bulgaria’s Grigor Dimitrov, while five-time Indian Wells champion Novak Djokovic beat Poland’s Kamil Majchrzak 4-6 6-1 6-2 to also reach the third round.
Spaniard Alcaraz won the Australian Open this year to become the youngest man to complete the career Grand Slam, and has won all 13 of his matches in 2026.
“I played great,” he said. “The conditions weren’t easy – a lot of wind today.”
Serb Djokovic, playing for the first time since losing the Australian Open final to Alcaraz, said: “I knew that the first match in such a long time will be a little bit tricky.
“I felt like I had to find my A-game when it was most needed, particularly the beginning of the third.”