Three match points slipped by for Shapovalov as Team World once again suffered an agonizing day-one defeat, going down 6-4 5-7 13-11.
“I guess Denis and me continued where the Laver Cup last year stopped,” said Thiem.
“It’s a really special thing with the tiebreak in the third, it creates lots of close moments and match points on either side. It’s also a little bit of luck at the end.”
Europe extends its unbeaten run in opening-day singles matches to seven and takes an early 1-0 lead in the race to the 13 points that will secure victory on Sunday.
I can’t imagine this is only the first match – we started like this, with many more to come – Bjorn Borg
In a packed arena at Palexpo, the third edition of the Laver Cup got under way with a clash between two of the best shot-makers in the game – and it was Thiem who prevailed.
The Austrian, ranked 28 places higher at No.5 in the world, needed one break of serve in the first set before Shapovalov fought back to take the second.
It was the Canadian who made the early move in the 10-point tiebreak but a whipped forehand down the line brought Thiem back on serve.
GALLERY: Laver Cup 2019 begins
Shapovalov appeared to have done enough when a burst of quality brought him two match points at 9-7, but a framed backhand and a forehand winner from Thiem squared it at 9-9.
Match points then went begging for both players before Thiem made the decisive move at 11-11, dominating the next two rallies and securing victory when Shapovalov netted a forehand.
“I knew before it’s going to be a great competition,” saud Europe captain Bjorn Borg.
“I can’t imagine this is only the first match – we started like this, with many more to come. Dominic played well and did a great effort to win this match.”
Jack Sock will attempt to get Team World on the board when he faces Europe’s Fabio Fognini in the second singles match of Friday’s afternoon session.