The Scot beat Moldova’s Radu Albot, who was trying to claim his 100th tour-level win, 6-4 6-3 in one hour and 42 minutes.
Murray had just 18 unforced errors to 35 for Albot, and never faced a break point on his serve while firing six aces.
Having won in straight sets for the first time since October, Murray tweeted: “I’d forgotten what that felt like. Bosh.”
The win set the Briton up to take on compatriot Jack Draper after the 21-year-old beat 24th seed Dan Evans 6-4 6-2.
Draper has lost just eight games through his first two matches of his Indian Wells debut.
There was more glory for Britain in the women’s draw with Emma Raducanu – the 2021 US Open champion – beating 20th seed Magda Linette 7-6 (3) 6-2.
‘I’d forgotten what that felt like,’ said Murray after his win over Radu Albot
/ USA TODAY Sports
Top-ranked Iga Swiatek routed Claire Liu in 65 minutes to win her opening match on Saturday.
Swiatek, the defending champion who took over the number one ranking nearly a year ago, won 6-0 6-1.
Carlos Alcaraz, the second-ranked men’s player, defeated qualifier Thanasi Kokkinakis 6-3 6-3, Taylor Fritz, the defending men’s champion, rallied past Ben Shelton 4-6 6-4 6-3, while Jannik Sinner defeated Richard Gasquet 6-3 7-6 (2).