Both players are scheduled to face each other in the fourth round and Ivanovic kept her part of the bargain with a second round 6-3 6-1 victory over France’s Aravane Rezai in the opening match at Arthur Ashe Stadium.
Wimbledon champion Williams followed her on to the show court and beat unseeded Romanian Ioana Raluca Olaru 6-4 6-2.
Ivanovic suffered an early hiccup when Rezai broke her service in the first game but the Serbian changed gear at 3-2, breaking back to win the next four games and take the set by serving out to love.
The winning streak continued in the second set as Ivanovic raced into a 3-0 lead before the Frenchwoman got on the scoreboard.
But the number five seed was quickly back in control and won the next three games to secure victory after an hour and five minutes on court.
The Serb said she was relishing the opportunity to play Williams, to whom she lost 6-2 6-4 in the Wimbledon semi-finals.
“It’s not a big secret that this part of the draw is much harder. There’s many good players,” Ivanovic said.
“Hopefully I can win my next match and then play Venus again. We had one tough match in Wimbledon.
“I would really be excited to play against her. I’ve never beaten her but I think this is a different tournament, different circumstances. I definitely have a chance.”
Two-time US Open winner Williams played well within her capabilities to beat Olaru, continuing her comeback from a left wrist injury.
In the first round she dispatched qualifier Kira Nagy of Hungary 6-2 6-1, throwing in a 129mph serve along the way, but there was no need to reach those heights as the Romanian surrendered tamely with two double faults in her final service game.
Like Ivanovic, top seed Justine Henin suffered a first-set break of service before turning up the pressure and blasting past her second round opponent.
The Belgian sealed her place in the third round with a 6-4, 6-0 defeat of qualifier Tsvetana Pironkova of Bulgaria.
After a straight-sets victory on Monday, 14th seed Elena Dementieva repeated the feat against unseeded Czech Petra Cetkovska, beating the qualifier 6-3 6-2 in an hour and 12 minutes on Court 11.