The Russian has struggled to find form this season, crashing out of the Qatar Open in the opening round.
Sharapova, a two-time victor in the California desert, was one of the event's major attractions after missing the last two editions, owing to her 15-month doping ban.
"I wanted to do well here and not just because I won this event a couple times", said Sharapova, who won the Indian Wells title in 2006 and 2013 but was unseeded for this year's event, having dropped to 41 in the rankings.
Meanwhile, Sam Stosur recovered after losing the first set to American Lauren Davis to win the game 3-6, 6-3, 6-3 and advance to the second round where she will face Kristina Mladenovic.
Democrat seeks businessman in Mueller probe
Nader is an adviser to Crown Prince Mohammed bin Zayed Al-Nahyan of Abu Dhabi, the de facto ruler of the United Arab Emirates. The meeting was a chance encounter not a planned discussion, Prince later described to congressional investigators.
In earlier action, American teenager Amanda Anisimova recorded her first top-level victory with a 6-2 6-2 thrashing of Pauline Parmentier.
In other matches on the first day of the two-week tournament, Belinda Bencic saved a match point in beating Timea Babos 1-6 6-1 7-6 (7-4), while wildcard Eugenie Bouchard lost to qualifier Sachia Vickery 6-3, 6-4.
"It's very exciting. I've worked really hard for this so I'm proud of myself", Anisimova told Tennis Channel, adding that adjusting to the senior ranks had been more mental than physical.
Sharapova made six double faults, won just 25 percent of her second serve points and had her serve broken five times. She trailed 4-1 in the first set before holding serve at 4-all. Serena Williams returns to the tour for the first time in 14 months Thursday when she plays a first-round match.