Svetlana Kuznetsova will now face British wildcard Tara Moore in second round. (Source: Reuters)

Russia’s Svetlana Kuznetsova got a late birthday present under Wimbledon’s centre court roof on Tuesday with a 7-5 6-4 win over former world number one Caroline Wozniacki, who is projected to drop out of the top 50 with the defeat.

The veteran 13th seed’s power undid the Dane, who had been seeking her first win at a grand slam this year after being dumped out of the Australian Open in the first round and missing Roland Garros due to injury.

The WTA women’s tour said the 25-year-old, rated the best in the world in 2010 and 2011, could drop as low as 59, depending on other results, when the new rankings are released the day after the men’s final.

Coming into the tournament ranked 45 after injuries to her ankle, knee and wrist, it was the first time Wozniacki, 25, had been unseeded at a major since the 2008 Australian Open and she was visibly gloomy after the match.

“It kind of just sucks right now to be out of the tournament. Yeah, there’s not really much else to say,” she told reporters.

“It’s been a tough year in general. It’s been some injuries, it’s been some bad draws.

“But, you know, you just have to keep fighting …and hope eventually that’s going to turn and you’re going to take the chances you’re going to get.”

The crowd was willing the Dane to take the match into a third set as former world number two Kuznetsova, who turned 31 on Monday, tightened up and looked like she might fritter away her lead.

But the Russian regrouped to serve out the match with a love game as Wozniacki sailed the ball long off her forehand.

“She stepped up … I got a bit tense and rushed a bit,” Kuznetsova said of her late wobble as the pair played on protected by the roof when all other matches were abandoned due to rain.

“It was my first experience of playing with the roof closed, the first time, it was really nice,” she said, adding she was happy not to have had to play on her on birthday.