Bouchard - the Canadian third seed - overcame Simona Halep in the Wimbledon semi-finals but injuries have plagued her since losing the final to Petra Kvitova last month.
However, the 20-year-old, who withdrew from the Citi Open and lost in the second round in both Montreal and Cincinnati after first-round byes, returned to the WTA Tour winners list with a straight sets demolition of Serbia's Jovanovski in just 52 minutes on Monday.
Bouchard sent down four aces and won six break points as she earned a second-round showdown with Australian wildcard Samantha Stosur, who survived to beat Japan's Kurumi Nara 7-6 (7-5) 6-7 (10-12) 6-2 in New Haven.
The head-to-head record between the pair is level at one win apiece.
"I'm looking forward to a battle," Bouchard said.
"We've had tough matches in the past. I know she'll try to take control with her serve and forehand.
"I'm going to look to try to take it early and control the point like I did today and really put pressure on her."
Four-time champion Caroline Wozniacki also progressed to the next round.
Wozniacki - the Danish fourth seed - lost the first set but fought back to topple Swiss qualifier Timea Bacsinszky 4-6 6-1 6-2.
There was no such luck for Slovak fifth seed Dominika Cibulkova and seventh-seeded Italian Sara Errani.
Cibulkova crashed out at the hands of Germany's Andrea Petkovic, losing 7-6 (7-2) 6-3.
Errani, meanwhile, was ousted by Garbine Muguruza of Spain 6-2 3-6 6-1.
In other results on Monday, Slovak Magdalena Rybarikova accounted for Spanish qualifier Silvia Soler-Espinosa 6-4 6-3.
Chinese qualifier Shuai Peng beat Ukraine's Elina Svitolina by the same scoreline.
Belgian wildcard Kirsten Flipkens prevailed 6-3 4-6 6-2 against Japanese qualifier Misaki Doi.
Barbora Zahlavova-Strycova emerged victorious against Swiss qualifier Belinda Bencic, winning 6-4 5-7 6-3 after more than three hours on court.
Meanwhile, French lucky loser Caroline Garcia edged Romanian qualifier Irina-Camelia Begu 7-6 (7-4) 7-6 (7-4).