Ivanovic has not played since Montreal three weeks ago because of a foot problem, and she could not have taken a break on a worse note after losing 6-0 6-0 to Roberta Vinci.
The Serb said: "In that first game I was like, 'Oh, my God at least I should win a game first'.
"In all seriousness, it wasn't easy, especially as it was one of my first matches on hard courts as well.
"It's a lot different. We have been playing on grass for a long time this season. Taking all into consideration, I'm really happy with today's [Tuesday's] performance."