Play continued at the All England Tennis Club club with defending women's champion Serena Williams moving on. Andy Murray was also victorious before the rains came.
Serena Williams was hardly at her best on Tuesday, but she didn't need to be against Switzerland's Amra Sadikovic, who was ranked 148 in the world and playing in her first Grand Slam event.
The American, who is seeking to draw level with Steffi Graf for the most women's majors won in a single's career, had troubles with her serve. But she still downed Sadikovic in straight sets 6-2, 6-4.
The 27-year-old Sadikovic retired from competitive tennis in 2014 but has since made a return.
"I never underestimate anyone," said Williams, who had only four aces to five double-faults. "It was a really good match but I don't think it was tougher than I thought. It was definitely tough, but I always expect the best from everyone."
It was Williams' 80th match victory at Wimbledon. It came the day after Garbine Muguruza, the woman who beat Williams for this year's French Open title, won her first-round Wimbledon match.
On the men's side, number two seeded Andy Murray of Scotland beat fellow Briton and practice partner 6-2, 6-3, 6-4. Murray didn't drop his service once in the match.
Fourth-seed Stan Wawrinka, a two-time Grand Slam winner, had significantly more difficulty with US teenager Taylor Fritz. But the Swiss eventually prevailed 7-6, 6-1, 6-7, 6-4.
Rains hit London late in the afternoon, delaying the matches not on Centre Court.