The eighth-seeded Belarusian had played only twice in the last six months because of an injury to her left foot.
"I'm so happy to get the win -- it's been a long time since I had that feeling," the 24-year-old told the BBC as she came off court.
Azarenka lost to Italian Camila Giorgi in the first round at Eastbourne last week but the three-set defeat did offer some invaluable grasscourt practice.
On Monday she looked comfortable in the first set against the 108th-ranked Croat, finding the lines with her powerful groundstrokes on both sides of the court.
Lucic-Baroni, 32, whose best performance at Wimbledon was a semi-final appearance 15 years ago, could not keep up, producing a string of errors in her attempts at winners.
Azarenka, letting rip her trademark wail of effort with every shot, had a characteristic lapse of concentration in the sixth game of the first set, dropping her serve with two double faults.
But breaks of the speedy Lucic-Baroni serve in the third, fifth and ninth games of the set saw her past the first hurdle.
The experienced Croat regained her composure in the second set, giving Azarenka a good baseline workout and exposing the rustiness of her opponent's months out of the game.
"The second set was a bit tricky," Azarenka said. "My game was a little up and down but I'm happy I stayed in there and fought for every point."
The Belarusian, Australian Open champion in 2012 and 2013, vented her frustration, thumping her racket on the ground and admonishing herself for more double faults.
But, with iron will, she saved a string of set points in the second set and kept her cool when a sick ball girl had to be led from the court in the final game of the match.
Lucic-Baroni valiantly resisted match points on her own serve but eventually crumbled in the face of Azarenka's power and resolve to send a ball long and concede the encounter in just over an hour and a half.
(Reporting By Clare Lovell; editing by Josh Reich)
Share
