Shakhtar Donetsk spoiled Real Sociedad's return to the Champions League after a decade-long absence when Alex Teixeira struck twice to give the more experienced visitors a 2-0 win in Group A.
The rain lashing down at the Anoeta stadium in the Basque city of San Sebastian initially did little to dampen the home supporters' enthusiasm as Sociedad took the game to the Ukrainian side and created a host of chances.
However, Teixeira opened the scoring for Shakhtar in the 65th minute, collecting a neat back flick from Douglas Costa before firing home.
The Brazilian then made sure of victory three minutes from time when he drove the ball into the far corner of the net from the left of the penalty area.
The win boosts Shakhtar's confidence for their next match at home to Manchester United in two weeks' time when Sociedad will attempt to revive their hopes of reaching the knockout stages with a trip to Bayer Leverkusen.
Sociedad were kicking themselves after squandering a series of goal-scoring opportunities including a header by Mexican forward Carlos Vela in the 73rd minute that cannoned back off the crossbar.
"In the first half we were the superior team but we didn't score and in the second we paid for that," captain Xabi Prieto told Spanish television.
"In the second half the team fell apart and we paid for the way we played," added Prieto who had a strong claim for a penalty waved away by the referee.
It was the Basque club's first taste of European competition since their debut in the Champions League group stage in the 2003-04 season when they finished second in their section before losing to Lyon in the last 16.
Shakhtar, the 2009 Europa League winners, are competing in the Champions League group stage for the ninth time.
"It's a tough loss, playing at home and returning to Europe after so many years," Vela said. "We need to learn from the mistakes and look to recover the lost points in the next match," the former Arsenal player added.
"They had two chances and made the most of them and killed off the game."