Blake, the top American competing in the Olympic tennis tournament, moved into the second round by defeating Chris Guccione of Australia 6-3, 7-6 (7-3).
Rain limited the opening day schedule to just nine matches and Blake had to wait more than two hours before his match could start. He will take on either Thomaz Bellucci of Brazil or Dominik Hrbaty of the Slovak Republic in the second round.
"It was a ton of emotions," said Blake, who made his Olympic debut. "It's a great feeling. Davis Cup is one thing, but it's the same kind of nerves when you're playing for something more than just yourself. It's a ton of fun."
Top seeds Roger Federer and Rafael Nadal will play Monday, weather permitting.
Ivanovic had been scheduled to play Cara Black of Zimbabwe in the first round.
"I've been struggling with the thumb," Ivanovic said. "We even flew a doctor in from Australia to help with the hand."