The Romanian, a hero of Raducanu, defeated Marta Kostyuk 7-6 (7-2) 6-1 in one hour and 33 minutes and will now take on the Briton's Belarussian conqueror in the next round.
Sasnovich, who is currently ranked No.100, beat Raducanu 6-2 6-4 in one hour and 25 minutes, ending her 10-match unbeaten run.
Halep, the No.11 seed, who split with long-time coach Darren Cahill last month amid an injury-disrupted year, was down a break early before working her way back and dominating the tiebreak.
Halep broke twice in a more controlled second set to claim victory in her 10th appearance at Indian Wells.
"I missed a lot playing tennis at this level this year because I've been injured and many months, I couldn't play matches," Halep, who won at Indian Wells in 2015, said.
"I came here a little more aggressive than normal and I'm trying to improve my game and myself."
Fellow two-time Major winner Petra Kvitova eased into the last 32 with a 6-2 6-2 triumph over Arantxa Rus from Netherlands.
No.7 seed Kvitova set up a showdown with two-time Australian Open champion Victoria Azarenka after she beat Magda Linette 7-5 3-0 in a walkover. Kvitova leads Azarenka 5-3 in head-to-head battles.
No.2 seed Iga Swiatek dominated Croatian Petra Martic 6-1 6-3 to seal her passage into the third round, while No.4 seed Elina Svitolina got past Teresa Martincova 6-2 7-5.
Beaten 2021 US Open finalist Leylah Fernandez triumphed over experienced Frenchwoman Alize Cornet 6-2 6-3 and will play No.9 seed Anastasia Pavlyuchenkova in the third round after she easily accounted for Madison Keys 6-3 6-1.