It was a pretty tricky first round for Williams - Vesnina had won their only two previous meetings, including a devastating first round loss at Wimbledon two years ago - but Williams was all over the Russian this time, blasting 10 aces and breaking serve four times en route to a 63 62 victory.
"The last couple matches I played against her, at Wimbledon she played so well and it wasn't my day, and Cincy as well - I had some chances there but she was clearly more on her game," Williams said.
"These days I'm a little more on mine, so I was glad to get a win."
Williams was asked about what she needs to do to get back to her best level. "I have to just keep playing and getting matches - there's no other way to it, really," she said. "In moments where I'm controlling the match, the better I'll feel. I feel like I've gotten a little rusty sometimes in those areas."
And on making her return to Dubai? "I'm just excited to be here," Williams said. "It's been a long time, and I just couldn't come, basically. So just to have a chance to come here is exciting for me.
"I feel like out of all the people in the draw, I'm the one that has my eyes widest open," she added. "Maybe there are a couple other players, like Kleybanova, who maybe have a similar perspective."
Williams conquered Dubai in back-to-back years in 2009 and 2010, but had to miss the last three years due to illness and injury. But after her win over Vesnina she has now won 11 matches in a row here, and 22 of 23 sets in that stretch, dropping just one set to Serena Williams in the 2009 semifinals.
"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."
Flavia Pennetta, Annika Beck, Karolina Pliskova and Maryna Zanevska secured spots in the main draw with wins in the final round of qualifying. Beck, who turned 20 on Sunday, couldn't have had a better 20th birthday present - she beat World No.19 Eugenie Bouchard, 61 64, for her first Top 20 win.