Hanescu won a set from Federer for the first time in their five meetings. But the challenge the Romanian seemed to be mounting against the world's top-ranked player by winning the final two points of the tiebreaker was dashed quickly in the final set.
Federer, a two-time champion of this event, lost five points while winning the first three games of the final set and just 13 points in all — including Hanescu's love service game for 3-1 — in the 23-minute set.
The Swiss star, who was playing his first match since winning the Australian Open Jan. 31, had 10 aces and hit 62 winners to offset 39 unforced errors. He will face No. 27 seed Marcos Baghdatis of Cypress in the third round.
"I was happy with the way I played," Federer said. "Not having played for so long, I thought it was a good match overall. Missed maybe some of the clutch serving when I really needed it, but that's something that happens."
Seventh-seeded Andy Roddick, Federer's potential opponent in the quarterfinals, beat qualifier Yen-Hsun Lu of Taiwan 6-4, 6-4 late Sunday night.
Also, No. 2 seed Caroline Wozniacki of Denmark beat Maria Kirilenko of Russia, 6-0, 6-3. Wozniacki, 19, is the tournament favorite following top-seeded Svetlana Kuznetsova's loss to Carla Suarez Navarro on Saturday. Wozniacki will face 16th seed Nadia Petrova of Russia in the fourth round.
Earlier, 2009 tourney runner-up Andy Murray beat Andreas Seppi 6-4, 6-4 in another second round match.
Murray, the No. 4 seed, was visibly unhappy with his play throughout the 86-minute match, repeatedly gesturing and talking to himself after errant shots.
Afterward the 22-year-old Scot headed for the practice court.
"It was a pretty scrappy match today," Murray said. "Even though it was relatively comfortable, still some tight moments. Then it was just to go and hit a few more balls and get used to the conditions.
"When you haven't played for a long time you have to expect not to play your best in the first match out. I'm sure next round out I'll feel fine."
The women's tournament that began with six former champions in the field is down to two following Zheng Jie's 6-3, 2-6, 6-3 win over Maria Sharapova, the 2006 champ. Sharapova, the 10th seed, lost the final four games after getting treatment on her right elbow while leading, 3-2, and preparing to serve in the third set.
Sharapova, who said she had trouble extending the elbow, had 14 double faults and lost serve seven times. Jie, an Australian Open semifinalist, lost serve six times.
The men's field lost No. 5 seed Nikolay Davydenko of Russia, who withdrew after tests revealed he had a fracture in his left wrist. He is expected to be sidelined for at least four weeks.
The beneficiary of Davydenko's misfortune is No. 29 seed Viktor Troicki of Serbia, who has played just one game but is in the fourth round. Troicki had a first-round bye and his opponent in the second round, Pablo Cuevas of Uruguay, withdrew after the first game of the match with a back problem.
No. 6 Robin Soderling of Sweden and No. 9 Jo-Wilfried Tsonga of France moved into the third round, but No. 12 Gael Monfils of France was beaten, 1-6, 6-2, 6-3, by Simon Gruel of Germany.
James Blake of the U.S. beat No. 13 David Ferrer of Spain, 6-1, 6-4.
In early third round women's matches, No. 4 seed Elena Dementieva was a 6-4, 6-2 winner over Kirtsen Flipkens of Belgium; and No. 5 Agnieszka Radwanska was a 6-1, 6-0 winner over Gisela Dulko, the Argentine who had beaten Justine Henin in the second round.
No. 11 Marion Bartoli ousted American Jill Craybas, 6-2, 6-0.