Seven-time grand slam winner Venus would face top-seeded world number one Serena in the last eight, should the three-time defending US Open champion win her fourth-round match against fellow American Madison Keys.
The 35-year-old Venus, seeded 23rd, overpowered 19-year-old qualifier Kontaveit, winning 84 percent of her first serves, breaking the Estonian four times and making only nine unforced errors in the 50-minute match.
Serena (33), who was following Venus on to the Arthur Ashe Stadium court, is trying to become the fourth woman to sweep all four grand slam singles titles in the same year after winning the Australian Open, French Open and Wimbledon this season.
Meanwhile, defending champion Marin Cilic was the first man through to the quarter-finals, taking down determined Frenchman Jeremy Chardy 6-3 2-6 7-6(2) 6-1 to extend his Flushing Meadows win streak to 11 matches.
Coming off a punishing five-setter with Mikhail Kukushkin in a third-round match that lasted four hours, Cilic took a while to find his power game but was unstoppable once he did, the ninth seeded Croat blasting 23 aces past 27th seed Chardy, who had no answer.
"Key today was finding my rhythm on the serve, especially towards the end of the third set," said Cilic. "I was having trouble a little with my movement after I twisted my ankle in the second set. That was causing me a little trouble, but in the end it's pretty good.
"I played really good in the fourth set, really great tennis, so I'm happy about it."
Cilic has found the defence of his title much tougher than winning, at least so far.
In last year's march to the title, Cilic recorded straight set wins over Tomas Berdych in the quarters, Roger Federer in the semi-finals and Kei Nishikori in the final.
This year, with the exception of a straight sets decision over Russian qualifier Evgeny Donskoy, all of Cilic's matches have gone four sets or more.
After splitting the opening two sets, Cilic's power began to show through particularly in the third set tiebreak when he used his big serve to full advantage firing four aces and going up 6-1 before closing out 7-2.
Cilic kept the pressure up, breaking the Frenchman in the fourth set, surging in front 5-0 and then serving out for the match.
"The fourth set was incredible serving, it can't get be better I guess," said Cilic. "I didn't lose too much energy today, so it's good news for me.
"Going to try and keep my streak going for a couple more matches."
