Sinner, back in the California desert after missing last year's edition, serving a drug suspension, controlled every aspect of the 64-minute contest in which he faced just one break point.
After Svrcina held serve for 1-1 in the first set, Sinner won nine straight games before Svrcina managed another hold. The Czech fought valiantly to force Sinner to serve it out, saving three match points in the final game before Sinner closed it with one more service break.
It was an auspicious start to a tournament in which the four-time Grand Slam champion's best runs ended in semi-final defeats to Carlos Alcaraz.
This year he can't meet top-seeded Alcaraz - or third-seeded five-time champion Novak Djokovic -- until the final.
"I feel mentally I'm in a good place," said Sinner, who lost to Djokovic in the semi-finals of the Australian Open and was surprised by Jakub Mensik in the quarters at Doha last month.
"I'm calm, I'm relaxed. But I'm also very happy to compete. We did a lot of work. Many, many hours on court. Many hours in the gym. I'm trying to get a little bit stronger."
Zverev defeats Berrettini
Fourth-seeded German Alexander Zverev breezed into the third round with a brisk 6-3, 6-4 victory over Matteo Berrettini.
Zverev didn't face a break point on a windy Stadium Court, breaking Berrettini's serve once in each set to polish off the victory in just one hour and 11 minutes.
It was an encouraging start for the German, who fell in his opening match last year in the California desert, where he has never made it past the quarter-finals.
"I am very happy with the performance," Zverev said. "He is somebody that is extremely aggressive, massive forehand, massive serve.
"When you back off a little bit, it is very difficult against him, but today I thought I was the one pushing, I was the one being aggressive."
Zverev hopes it's a harbinger of things to come.
"I have struggled in Indian Wells before, but I feel different this year," he said. "Hopefully, it is going to be a different result, and it was a good start."
Sabalenka swats Sakatsume, Osaka beats Kasintseva
Sabalenka, playing her first tournament since a runner-up finish to Elena Rybakina at the Australian Open, took on Japanese qualifier Himeno Sakatsume not long after Zverev's victory, winning 6-4, 6-2 in a little over an hour.
"I'm really happy with the way I was serving, with the way I was putting her on the back foot," said Sabalenka, who has twice reached the Indian Wells final but lost to Rybakina in 2023 and to Mirra Andreeva last year.
Japanese superstar Naomi Osaka, seeded 16th in her first tournament since withdrawing from the Australian Open with an abdominal injury, defeated qualifier Victoria Jimenez Kasintseva 7-5, 6-2.
Gauff and Shelton hold down homefront
Women's fourth seed Coco Gauff rallied from two breaks down in the second set for a 6-3, 7-6(5) victory over qualifier Kamilla Rakhimova.
Rakhimova, ranked 88th, served for the second set three times, wasting one set point. She led Gauff 5-4 in the tiebreaker before the American reeled off the last three points.
"I felt like if I could get into the tiebreaker, I feel like I have a pretty good tiebreak record," Gauff said. "I knew the odds were in my favor when the tiebreaker started."
Ailing eighth seed Ben Shelton clawed out a 6-7(3), 7-6(4), 6-3 victory over Reilly Opelka in an all-American clash.
Shelton trailed 4-5 in the second-set tiebreaker, but Opelka dropped two points on his own serve, and Shelton held on to level and capture the third set with one more moment of drama when he took a hard fall in the final game.
Hungarian veteran Marton Fucsovics pulled the first big upset, ousting fifth-seeded Italian Lorenzo Musetti 7-5, 6-1.
It was another disappointing setback for Musetti, who was playing his first tournament since he retired with a right leg injury while leading 24-time Grand Slam champion Djokovic by two sets in the Australian Open quarter-finals.
Mboko and Raducanu advance
In other early matches, Canadian teenager Victoria Mboko, playing her first since cracking the top 10, beat Australian Kimberly Birrell 6-4, 7-6(5).
"It's my first time playing here, so a lot of emotions," said Mboko, whose rise to 10th in the world was cemented with a runner-up finish in the 1000-level event in Doha last month.
"I feel like I've learned a lot in the past year, and I'm still learning. It's just upwards."
Britain's Emma Raducanu, seeded 25th, was quick out of the blocks with a 6-1, 6-3 victory over qualifier Anastasia Zakarova.
Raducanu, ousted in the second round of the Australian Open, arrived in California buoyed by a runner-up finish last month in Romania, where she reached her first final since her upset triumph at the 2021 US Open.
Follow the men's side at Indian Wells here, and the women's here.