While the Swiss world number one had to work harder than expected in his first match back since winning the Australian Open in January, Britain's Andy Murray shook off a bit of rust to outclass Italian Andreas Seppi 6-4, 6-4.
In other matches, sixth seed Swede Robin Soderling crushed Evgeny Korolev of Kazakhstan 6-2, 6-4 and seventh-seeded American Andy Roddick eased past qualifier Lu Yen-hsun of Taiwan 6-4, 6-4.
Federer, seeking a record fourth title at Indian Wells, appeared on track for a clinical victory when he broke Hanescu in the second game before winning the opening set in 30 minutes.
However, the 16-time Grand Slam champion was surprisingly broken in the sixth game of the second when the Romanian struck a backhand return winner down the line.
Although Federer fought back to 6-6, he fell behind 0-3 in the tie-break, which Hansecu won 7-5 to level the match when the Swiss hit a backhand long.
Federer broke his opponent in the second and sixth games to seal victory. He will next meet 27th-seeded Cypriot Marcos Baghdatis. Murray, although not at his very best, broke Seppi in the seventh game of the second set when the Italian pushed a backhand volley wide before wrapping up the win.Meanwhile, fifth-seeded Russian Nikolay Davydenko pulled out because of a broken left wrist.
Davydenko first suffered the injury last month in Rotterdam but it was misdiagnosed and the fracture was only revealed after an MRI scan on Sunday, an ATP Tour official said.
Zheng surprise
Former champion and 10th seed Maria Sharapova of Russia was knocked out, losing an error-strewn marathon to China's Zheng Jie 6-3, 2-6, 6-3 in women’s play.
While Sharapova made a premature exit, it was plain sailing for second-seeded Dane Caroline Wozniacki, who hammered Russian Maria Kirilenko 6-0, 6-3, and Elena Dementieva of Russia, who eased past Kirsten Flipkens of Belgium 6-4, 6-2.
Zheng broke Sharapova three times in the final set before clinching victory in a little under three hours with a searing forehand winner that clipped the baseline.
The 26-year-old Chinese, seeded 18th, booked a place in the fourth round against Australian wild card Alicia Molik, a 6-0, 6-2 winner over British qualifier Elena Baltacha.
Earlier, fifth seed Agnieszka Radwanska of Poland swept aside 31st-seeded Argentine Gisela Dulko 6-1, 6-0 and 11th-seeded Frenchwoman Marion Bartoli crushed American Jill Craybas 6-2, 6-0.
Paes, Bhupathi ousted
Leander Paes and Mahesh Bhupathi suffered shock first-round defeats along with their respective partnersThird seeds Paes and Czech Lukas Dlouhy went down fighting 4-6, 6-3, 6-10 to Spanish wild card pair of Rafael Nadal and Marc Lopez on Sunday night.
Bhupathi and his Belarusian partner Max Mirnyi, seeded fourth, lost a closely fought first round 4-6, 4-6 to Igor Andreev of Russia and Evgeny Korolev of Kazakhstan.