Twelfth seed Ivanovic blew by Sweden's Sofia Arvidsson 6-2 6-2 in 64 minutes, while Jankovic, seeded 27th, had a little more difficult time in stopping Lara Arruabarrena-Vecino, 6-4 6-2.
On the men's side, Frenchman Jo-Wilfried Tsonga became the first high-profile casualty when he was upset 6-4 1-6 6-1 6-3 by Slovakian Martin Klizan in a second-round match.
Serena Williams, the fourth seed looking to build on her Wimbledon and Olympic titles, plays Spain's Maria Jose Martinez Sanchez later Thursday, while world number one Roger Federer battles Bjorn Phau of Germany.
Ivanovic opened the day's programme before a sparse crowd on Arthur Ashe Stadium, while Jankovic played on outside court 17, a far cry from when they were both title contenders.
Arvidsson's counter-punching groundstrokes did little to offset the arsenal of Ivanovic, who is looking to advance to the quarter-finals for the first time at Flushing Meadows.
"I'm very happy about today's match because she's a tough opponent," said Ivanovic, who enjoyed a 39-7 advantage in winners. "She does retrieve a lot of balls. She likes to use pace off an opponent... I'm very pleased."
Jankovic took advantage of 39 unforced errors by her Spanish rival to win in one hour, 45 minutes.
"She was a tough opponent, she has a Spanish game," said Jankovic, in reference to Arruabarrena-Vecino's penchant for top-spin groundstrokes featuring long rallies.
"She has that good forehand with a lot of spin. She's very solid off the ground. She wasn't giving me any easy points. I had to work hard for each one."
Ivanovic, the 2008 French Open winner who is nursing a foot injury, said she is hungry to give herself a shot at winning another grand slam.
"It's been a long process of getting my mind there and my body and game and everything together," she said.
