Kanepi, who reached the final eight at the clay court Grand Slam in 2008 and 2012, was originally set to face Caroline Wozniacki, but the former World No.1 had to pull out due to a left wrist injury.
"It's disappointing for me to withdraw - it's a tournament I'm always looking forward to playing - but I knew I wouldn't be able to perform my best," Wozniacki said. "I also have to watch out for my wrist, so it doesn't get worse. I still have a long season ahead of me and it's important I'm healthy for that.
"But it's a wonderful tournament and everyone loves playing here, and I'll be back next year."
In stepped Konta, though, a British lucky loser. Kanepi had never played her before, and it showed at times, as she fell behind by a break early on in both sets - but the Estonian powered back both times, eventually moving into the next round in a tight two-setter in an hour and 34 minutes, 76(4) 64.
"It was my first match on clay in some time, so it felt a bit slippery at times, but I was happy with my serve," Kanepi said. "Johanna played very, very well though. I'm happy to get to the next round."
Perhaps surprisingly, Kanepi is making her career debut at the Premier-level event in Stuttgart.
"It's my first time here," she said. "Someone told me it's the best tournament of the year and that they take really good care of the players here, and I do feel really welcome here. It's just perfect."
The qualies also wrapped up on Monday, with Annika Beck, Ajla Tomljanovic, Gioia Barbieri and Diana Marcinkevica all moving into the main draw. Tomljanovic edged Mona Barthel in a third set tie-break.
"Mona is a very talented player," Tomljanovic said. "I thought it was a bit up and down from both sides today, but I'm happy with my serve and the way I fought, and hopefully I can keep going like this."
Barbieri actually beat Konta, who - as mentioned above - eventually got in as a lucky loser.
Now in her first WTA main draw, Barbieri will play two-time Grand Slam winner Svetlana Kuznetsova.
"I'm happy to play against Svetlana Kuznetsova," the Italian said. "It's just really nice to see my name next to hers. I am sure I will be nervous, but it's going to be a great experience for me.
"I'm crazy about tennis. When I go on court, I feel like a kid on Christmas Day."