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Dubai, United Arab Emirates (SportsNetwork.com) - Two-time champion Venus Williams was a first-round winner, while her world No. 18 fellow American Sloane Stephens exited the draw Monday at the $2 million Dubai Tennis Championships.

The 33-year-old former world No. 1 wild card Williams handled Russian Elena Vesnina 6-3, 6-2 for her 11th straight match win in Dubai.

The veteran American titled here back-to-back in 2009 and 2010, but then missed the 2011-13 editions to due injury and/or illness.

Meanwhile, Stephens gave way to Czech Lucie Safarova 6-3, 7-5 on the hardcourts at Dubai Tennis Stadium.

"It was a tough match. She's a great player and she played really well," Stephens said. "I didn't really get a good rhythm today, and she was playing some really good tennis at the end of the match."

Also on Day 1, Ekaterina Makarova outlasted fellow Russian Alisa Kleybanova 6-4, 6-7 (3-7), 6-4, Spaniard Carla Suarez Navarro handled wild card and former top-10 Russian Nadia Petrova 6-3, 6-2, and Romanian Sorana Cirstea rolled past Italian Roberta Vinci 6-4, 6-3.

This week's top seed is reigning U.S. and French Open champion Serena Williams, who will open her Dubai stay against Makarova on Tuesday after enjoying an opening-round bye.

In some more first-round action on Tuesday, fifth-seeded former No. 1 Jelena Jankovic and eighth-seeded former top-ranked star Caroline Wozniacki will take to the courts.

Former Wimbledon champ Petra Kvitova, seeded third this week, beat former French Open finalist Sara Errani in last year's Dubai finale.