Eighth seed Wozniacki was dominant in beating Lucie Safarova 6-2 6-2 although the Dane lost her serve at 5-1 in the first set before breaking back immediately.
Safarova double-faulted to gift the world number 10 a 3-1 lead in the second set and the Czech capped a miserable display with a shanked forehand to cede the match to Wozniacki.
"I'm really enjoying the tennis and am happy to be out there - at one point it was just a job but I feel like I've got that hunger back and that enjoyment of the game," said Wozniacki.
The Dane ended 2010 and 2011 as the top-ranked women's player, but endured a tough 2012, slipping down the standings as she made little impression at the grand slams.
This year has also proved difficult for the 22-year-old, who has gone beyond the last 16 in only one tournament, and she will now face Chinese qualifier Jie Zheng before a potential showdown with new world number one Serena Williams in the quarter-finals.
Williams, who got a bye into the second round, will play France's Marion Bartoli on Wednesday.
Grand Slam winners Samantha Stosur and Petra Kvitova strolled into the second round of the Dubai championships with straight sets wins while Australian Open champion Victoria Azarenka withdrew due to a foot injury.
Australian seventh seed Stosur beat Russia's Ekaterina Makarova 6-3 6-1 after suffering one wobble on the way when she lost her serve to fall 3-2 behind in the first set after slugging an easy cross-court smash wide.
However, that shocked the 2011 US champion into action and Stosur then won 10 out of 11 games as her opponent wilted.
Makarova, 24, scuffed a backhand into the net to lose the first set, while the second was a formality for Stosur.
"The first couple of games were good - I was getting ahead in the games but not winning them - and then I got down that break and that kicked me into gear," Stosur said.
"It wasn't like anything outstanding, but I played tight games and didn't really give her too much."
Czech Petra Kvitova put an indifferent start to 2013 behind her as she thumped Daniela Hantuchova 6-2 6-1.
Kvitova won Wimbledon in 2011, but suffered a second-round exit at January's Australian Open.
"At the beginning of the season I wish (I had) better results," Kvitova said. "I changed my fitness preparation, so I needed some time to get used to it."
Sara Errani held her nerve to come through a tough opening match at WTA Dubai as she was pushed all the way by Julia Goerges.
World number seven Errani had to save three break points to win the opening set, but 20th-ranked Goerges hit back to force a decider.
It was Errani who held her nerve in the final stages, however, saving both break points that Goerges earned against her and grabbing one of her two chances to clinch the match and earn a second round clash against Sorana Cirstea.
WTA Dubai results:
7-Samantha Stosur (Australia) beat Ekaterina Makarova (Russia) 6-3 6-1
Roberta Vinci (Italy) beat Svetlana Kuznetsova (Russia) 6-3 6-2
8-Caroline Wozniacki (Denmark) beat Lucie Safarova (Czech Republic) 6-2 6-2
Zheng Jie (China) beat Urszula Radwanska (Poland) 6-2 2-6 7-5
6-Petra Kvitova (Czech Republic) beat Daniela Hantuchova (Slovakia) 6-2 6-1
Nadia Petrova (Russia) beat Dominika Cibulkova (Slovakia) 5-7 6-3 6-2
5-Sara Errani (Italy) beat Julia Goerges (Germany) 6-3 4-6 6-4
WTA Memphis results:
Jamie Hampton (U.S.) beat Coco Vandeweghe (U.S.) 6-3 6-0
7-Magdalena Rybarikova (Slovakia) beat Lauren Davis (U.S.) 7-6(2) 6-2
Andrea Hlavackova (Czech Republic) beat Melanie Oudin (U.S.) 6-4 3-6 6-3
Claire Feuerstein (France) beat 5-Lucie Hradecka (Czech Republic) 6-3 6-4
3-Sabine Lisicki (Germany) beat Madison Keys (U.S.) 7-5 6-3
WTA Bogota results:
5-Flavia Pennetta (Italy) beat Alexandra Panova (Russia) 4-6 6-3 6-3
4-Francesca Schiavone (Italy) beat Sharon Fichman (Canada) 4-6 6-4 6-4
Karin Knapp (Italy) beat Eva Birnerova (Czech Republic) 6-1 6-1
Lara Arruabarrena Vecino (Spain) beat Yuliana Lizarazo (Colombia) 6-2 1-6 6-3
Teliana Pereira (Brazil) beat Yvonne Meusburger (Austria) 6-3 6-3
8-Timea Babos (Hungary) beat Beatriz Garcia Vidagany (Spain) 6-4 1-6 7-6(4)
Tereza Mrdeza (Croatia) beat 7-Pauline Parmentier (France) 7-6(5) 6-4
3-Lourdes Dominguez Lino (Spain) beat Catalina Castano (Colombia) 3-6 6-2 6-1
Maria Teresa Torro (Spain) beat 6-Arantxa Rus (Netherlands) 6-4 6-3
Alexandra Cadantu (Romania) beat Maria Joao Koehler (Portugal) 6-0 6-3