The 20-year-old Dane lost the top spot only on Monday, but she will claim it back when the new rankings are released next week after seeing off Peer 6-2, 6-4. Wozniacki will take on the former No. 1 Jelena Jankovic, who beat fourth-seeded Samantha Stosur 6-3, 5-7, 7-6 (4).
Svetlana Kuznetsova beat eighth-seeded Agnieszka Radwanska of Poland 7-6 (7), 6-3, and will play the 11th-seeded Flavia Pennetta of Italy who beat Alisa Kleybanova of Russia 6-2, 6-0.
"Of course, it's nice to be back to No. 1," Wozniacki said. "It's a good feeling. I gave Kim one week.
Hopefully, now I will have it for a few more weeks." The WTA said Wozniacki will stay at No. 1 for at least four weeks until March 20.
After her short stay at the top came to an end, Clijsters posted a brief message to Wozniacki on her Twitter page: "Congrats :-) ha ha." Wozniacki became the first player from Denmark to hold the No. 1 ranking when she toppled the injured Serena Williams in October and remained there for 18 weeks.
But she has yet to reach a Grand Slam final, most recently losing to Li Na of China in the Australian Open semifinals in January.
However, last year she won more tournaments than anyone else with six. Peer said she was a deserving No. 1, noting that Clijsters also held the top spot before she won the first of her four Grand Slams.
"It's not like she put in the computer her name as No. 1," she said. "She won so many tournaments. I am sure she will (win a Grand Slam) ... She is putting so much work, and she's not just boom, No. 1." Wozniacki appears in good form in Dubai, easily beating an ailing Anna Chakvetadze and then only dropping a game in her third round match against Japanese qualifier Ayumi Morita.
"I'm playing good tennis," Wozniacki said. "I feel when I'm playing on a high level, I'm tough to beat. So, I'm really pleased about the way I'm playing at the moment." Her win on Friday ended another strong run from Peer, who two years ago was barred from playing in Dubai because of nationality. The Israeli player is still given extra security and isolated from the other players in a guarded compound.
Last year, Peer reached the semifinals, beating Wozniacki on the way. This time around, Wozniacki went up early 3-0 in the first set and was never seriously challenged mostly due to the erratic play of the Israeli who had 34 unforced errors - more than twice that of the Dane.
"I played two games good in the first set and only last three or four games in second set. Between that, I played pretty terrible," Peer said. "I don't think she had to do anything, just be there and put the balls in.
I finished much better than I started." The controversy over Peer in Dubai has died down somewhat and the 23-year-old Israeli said Friday she "hopes to come every year" to the tournament. Peer said she felt "comfortable and safe," although she still hasn't played on the venue's center court.
"It's something that I dream of," she said. "I wish one day I'm going to play in the center court. It means I need to get to the finals probably." While Wozniacki's match was mostly one-sided, Jankovic's nearly three-hour affair with Stosur was probably the most entertaining of the tournament.
In the decider, Stosur went up 3-0, 4-1 and 5-3, but Jankovic kept finding a way back into the match before she eventually won the tiebreaker 7-4.
"It's been an amazing match," said Jankovic, who also came from 5-3 down in the final set against Kaia Kanepi of Estonia on Thursday. "I was a little bit tired on the court and I felt that I almost had no gas in the tank. But with positive attitude, I just kept saying to myself, just keep going one point at a time."