Nadal won his first set against Gilles Muller 7-6, with 8-6 in the tiebreaker, yesterday afternoon before rain stopped play.
Opening the action on Court No.1 this afternoon, he took the first set 7-6 with another tiebreaker, won 7-5. He sealed the victory with a comfortable 6-0 win in the final set.
"It was a very difficult match to play, especially the first two sets," Nadal said afterwards. "I'm happy about how I played the tiebreakers and very happy with the match [overall]."
Nadal appeared to suffer a groin injury towards the end of the first set yesterday but said he played "with no problems" today. He added that he expected to recover in the next two days before his fourth round match on Monday, most likely against the Argentinian Juan Martin Del Potro.
Meanwhile, Wozniacki defeated Australia's Jarmila Gajdosova in straight sets, 6-3 6-2, in one hour six minutes of play on centre court.
"I was real pleased today," she said afterwards. "She's a good player - a big serve and a big forehand - so it was very important for me to keep my focus and keep going."
Looking ahead to her fourth round draw against Dominika Cibulkova, she added: "My next round will be a tough one. She's a player that likes the courts fast. She attacks it. For me it will be important to keep my serve going."