Mirjana Lucic-Baroni dug deep in her first-round clash at the Connecticut Open, while Alize Cornet handed a double bagel to Yulia Putintseva.

Struggling with a shoulder injury in recent months, Lucic-Baroni battled past Anett Kontaveit 6-4 6-7 (3-7) 6-3 in New Haven on Sunday.

Lucic-Baroni suffered first-round exits in Toronto and Cincinnati but the 2017 Australian Open semi-finalist finally had something to cheer about against the world number 28 at the WTA Premier tournament.

"Really tough match, really tough first round," said Croatia's Lucic-Baroni, who will face either Katerina Siniakova or Peng Shuai in the next round. "I think she's playing the best she's played.

"It was a bit up and down, I was getting a bit frustrated with myself not being able to keep the one level the whole time but she picked up and played better so I was really happy overall that I was able to lift the level at the end to get the win.

"It hasn't been a secret that I've been struggling with my shoulder a lot and haven't been able to play. I know I'm playing good, I know I'm fit, I'm strong but it's difficult when your body's not letting you do what you want to do.

"Lucky I'm tough, I'm strong, I'm stubborn. It's been a couple of months but I got my win and now it's like I can relax, it's good."

It was far more straightforward for Frenchwoman Cornet, who blitzed Putintseva 6-0 6-0.

Cornet claimed six breaks of serve to dismantle the Kazakh in just 60 minutes.

Up next for Cornet in the second round is 2014 Australian Open runner-up Dominika Cibulkova.