Roger Federer, bidding for a fifth successive Wimbledon title, made short work of Russian debutant Teimuraz Gabashvili 6-3, 6-2, 6-4 to register his 49th straight win on a grass court.
However, his Swiss compatriot Martina Hingis was given a huge scare by a player ranked No. 233 in the world.
"It was difficult. There was a constant breeze from one end," Federer in reference to the building work at the famed show court, which is now completely uncovered in readiness for a long-awaited retractable roof.
"I prefer the old center court, but it's a work in progress," he said.
On Court 2, the so-called Graveyard of the Champions, Hingis found herself on the brink of suffering an embarrassing defeat.
The ninth seed had to save two match points against British wildcard Naomi Cavaday, who was playing in only her second Grand Slam match, before coming through with a 6-7 (1/7), 7-5, 6-0 win.
Hingis, who was the youngest champion of the Open era when she beat Jana Novotna as a 16-year-old in the 1997 final, will face Japan's Aiko Nakamura.
But she had to fight hard to stay in the tournament and her lack of fitness, which was caused by not playing for six weeks after suffering a hip injury in Berlin six weeks ago, showed in the early stages.
She squandered three set points in the opener before the 19-year-old Cavaday began to tire after failing to convert two match points in the 10th game of the second set.
Hingis, the ninth seed, then ran away with the match, sealing the win with a dominating third-set performance that was wrapped up in just 20 minutes.
"You couldn't get any closer to losing than being two match points down," Hingis said.
"But I had three set points in the first set and I was still serving," she said. "It's not like she was serving it out."
Federer, playing for the first time since his French Open final loss to Rafael Nadal, showed little sign of rustiness against Gabashvili in a 92-minute win.
Top seed Federer, who is hoping to match Bjorn Borg's five straight wins from 1976-1980, will now face either Argentine teenager Juan Martin del Potro or Davide Sanguinetti of Italy.
Third seed Andy Roddick, fresh from a fourth Queen's Club title, defeated Justin Gimelstob 6-1, 7-5, 7-6 (7/3) and now meets Thailand's Danai Udomchoke.
More than four hours of play was lost to rain on Monday, but French Open champion Justine Henin, looking to win a first ever Wimbledon title, did her bit to hurry things along with a 6-3, 6-0 win over Argentine qualifier Jorgelina Cravero in just 55 minutes.
Two-time champion Serena Williams enjoyed a rain-interrupted 7-5, 6-0 win over Lourdes Dominguez Lino of Spain and now takes on Australia's Alicia Molik.
British hopes, already subdued by the withdrawal of Andy Murray, were left on a knife-edge when veteran Tim Henman, a four-time semi-finalist, was level with Spain's Carlos Moya.
The match was two sets apiece with the final set poised at 5-5 when play was halted because of bad light.