Williams, a two-time U.S. Open champion, coasted to a 6-2, 6-3 victory over Germany's Julia Goerges in second-round play at Flushing, N.Y.
The No. 6 seed needed 79 minutes to dispatch Goerges and advance to a third-round matchup against 10th-seeded Karolina Pliskova of Czechoslovakia.
Williams, a four-time finalist in this event who needed three sets to win her first-round match, became the fifth woman to reach 70 wins in the event.
She needs three more victories to tie Steffi Graf for No. 4 all-time on the wins list at the U.S. Open.
Meanwhile, Venus' sister, Serena, defeated fellow American Vania King, 6-3, 6-3, to continue her string of having never lost before the third round of the U.S. Open.
"Hopefully I'll be able to play better as the tournament goes on," Serena Williams said on court after the match, which was completed in 64 minutes,
The top seed, Serena is aiming for her 23rd grand slam.
Fifth-seeded Simona Halep also advanced to the third round in straight sets with a 6-3, 6-4 victory over Lucia Safarova in the first women's match to be played under the new roof at Arthur Ashe Stadium.
A semifinalist here last year, Halep moved on to play Timea Babos, a 6-2, 6-4 winner over Richel Hogenkamp.
"It was not an easy match. It was difficult," Halep said. "At one point I lost the rhythm a little bit because she's left handed, not easy to play against. I knew that she's very tough. She's fighting till the end."
In other action, No. 4 seed Agnieszka Radwanska of Poland held off Britain's Naomi Broady, 7-6, 6-3, to move into the third round.
No. 15 seeded Timea Bacsinszky of Switzerland was upset by American Varvara Lepchenko in three sets, 6-4, 4-6, 6-4. The two-hour and 33-minute match was delayed on and off by rain.
Also, No. 16 Samantha Stosur defeated doubles partner Zhang Shuai in straight sets, 6-3, 6-3.