It was Nadal's first singles match since the 38-year-old fell in the opening round at Roland Garros on May 27, and he eased to a 6-3, 6-4 win in wet conditions.
Both Nadal and the 21-year-old Borg, currently ranked 461 in the world, were wild card entries to the Swedish clay-court tournament.
Despite an early scare with the former world number one slipping on the wet white line, Nadal broke for 3-1, hitting four aces to take the first set in 43 minutes.
An immediate break gave the Spaniard a foothold in the second, sealing the match on his second match point after 1hr 25min on court for his eighth ATP tour match win this season.
"It's good, I'm finally defending my title," joked Nadal, who has not played in Bastad since winning the title aged 19 in 2005.
"I haven't been playing a lot of tennis in the last few months.
"The feelings are great, playing on front of a full crowd means a lot to me and lucky to have been able to play without rain.
"Even in the tougher moments, I have been able to keep going with the help of the team, but of course the fans have a huge impact on that. They give me amazing energy."
The 22-time Grand Slam winner praised his rival, the son of the long-retired former world number one Bjorn Borg, now 68.
"It's a huge honour to play against the son of one of the biggest legends in the history of our sport," said Nadal.
"I think he played quite well, he has a great future in front. I wish him all the very best."
Nadal will next play fifth seed Cameron Norrie in the second round after the British player beat Slovak Jozef Kovalik 7-6 (7/4), 6-4.
Nadal skipped Wimbledon to focus on the Olympics which will be played at Roland Garros where he won 14 French Open titles.
On Monday, Nadal also teamed up with Casper Ruud for a doubles win on clay in Bastad two weeks ahead of the Paris Games.
Top seed Andrey Rublev starts his campaign on Wednesday against 121st-ranked Thiago Tirante of Argentina.
