Jovanovski was down a set and a break before turning the tide and winning the second set. She was in control throughout the third set, getting out to a 4-1 lead and breaking serve three times en route to her 4-6, 7-5, 6-3 win - her third straight in her head-to-head with the Romanian.
"Sorana is a tough player," Jovanovski said. "You need to be focused, play aggressively and not give her chances because she can always come back. I played well today, especially in the third set."
Jovanovski has been a three set specialist of late, winning three of them en route to the Baku final last week, and winning two already this week - having barely edged Olivia Rogowska in her Washington DC opener on Tuesday.
"It's difficult because I'm tired and jetlagged after playing in Baku and then flying here and going three sets in both matches," Jovanovski said. "But I fought until the end and am really happy."
"It was such a tough match," Mladenovic said. "Taylor played some unbelievable tennis today. She is very talented. I had already heard a lot about her and knew it would be a very difficult match. Plus, she's a lefty, which is one more thing to worry about. She broke me early in both sets, but I kept fighting and came back and played well. I served especially well, which I think was the key.
"I had such a tough draw playing Lucie in the first round. I've been trying to stay focused and play one match at a time. I'm just happy to be here enjoying my first time in Washington."
As for Nara, she was down a set and a break against Zarina Diyas, then reeled off 10 straight games before Diyas retired with a right elbow injury down 3-6, 6-2, 4-0.