"We are both the best players on the tour right now," said Serena, who is 9-9 against her older sister. "Obviously, we both are also playing our best tennis right now, which definitely makes our matches more exciting."
Ivanovic, a former top-ranked player, tried to unsettle Serena with an attacking game at the Aviation Club.
"She was really trying to hit hard," said Serena, who won the Australian Open last month. "I think her goal was to go for broke. I was feeling a bit tired at the start of the second set but wasn't too worried about her going 3-0 up as I knew I was just a break down. I knew I could pull it off."
Venus raced to a 3-0 lead in the first set and in the second broke her opponent again when the fourth-seeded Russian double-faulted in the seventh game.
"She has been playing great this year and she is a great player," Venus said. "She likes to control the match, and I also like doing the same. So I am pleased that I was able to do that."
Kanepi, who eliminated third-seeded Jelena Jankovic in the third round, has twice reached a WTA Tour final but has yet to win.
"It was difficult to play her as she hit some very uncomfortable shots for me, very low balls," Kanepi said of Vesnina. "I was rushing a bit, but I am glad I pulled it off. I think it is very possible that I can reach the final. But I am taking it one match at a time, so we'll see."
The Dubai Tennis Championship attracted a quality field this year, with nine of the WTA Tour's top 10 players in the draw. But it was overshadowed by the refusal to allow Israeli player Shahar Peer into the country. Organizers said they feared fan anger over Israel's recent military offensive in the Gaza Strip would spill into riots in the Arab country if Peer were to play.
On Thursday, however, the country said it was issuing a special permit for Israeli tennis player Andy Ram so he can play in next week's men's tournament.