After a winless debut season that saw them finish last among the five teams, Boston kicked off their second campaign on a high note at SoFi Center.
Thorbjornsen, stepping in for Adam Scott and Hideki Matsuyama, who were unavailable, delivered the decisive moment on the final hole, sinking a 15-foot eagle putt in his singles match against Sahith Theegala to secure the win.
Rory McIlroy, paired in singles against Ryder Cup teammate Justin Rose, added a crucial point with a birdie at the 10th hole, having earlier given Boston a 4-3 lead during the triples by sinking a difficult putt to claim the Hammer.
The McIlroy-Rose singles clash recalled their dramatic Masters play-off last April, which McIlroy won to complete his career Grand Slam.
"It's been a long time coming for Keegan [Bradley] and I to get a win," said McIlroy after the win.
"Lot of quality shots, a lot of birdies and eagles and Hammers thrown and bullets dodged. It was back and forth. It was certainly fun to play."
Michael Thorbjornsen made history as the first TGL player to sink four putts from beyond 10 feet in a single match, giving Boston a 6-5 edge when he drained a 17-foot putt on the 12th hole against Theegala. He soon followed that with a 15-foot birdie to seal the team’s first-ever victory.
Despite seeing his opening shot in the triples land in a bunker, the 24-year-old bounced back impressively and dominated the rest of his match.
Rory McIlroy described the Ryder Cup atmosphere at Bethpage Black as "by far the worst" he has experienced, adding that USA captain Keegan Bradley "could have done more" to address it.
Billy Horschel delivered a dramatic final-hole eagle to help Atlanta Drive GC start their TGL title defence with a 6-4 win over New York Golf Club.
Rory McIlroy has been named BBC Sports Personality of the Year after a landmark season in which he finally triumphed at the Masters and helped Europe secure a rare Ryder Cup victory on American soil.
Scottie Scheffler edged out Rory McIlroy in a play-off to claim victory at the first-ever Golf Channel Games, held at Trump National Golf Club Jupiter in Florida.
