Brazilian midfielder Alex Teixeira struck twice in the final 25 minutes to hand Shakhtar Donetsk the perfect start to their Champions League campaign with a 2-0 win at Real Sociedad.
The Basques had enjoyed the better of the early exchanges in their first appearance in the competition for a decade and were unfortunate not to be awarded a penalty when Darijo Srna felled Xabi Prieto inside the area in the first half.
Shakhtar have reached the last 16 of the competition in two of the last three years and their greater experience at this level shone through in the second period.
They counter-attacked to deadly effect and Teixeira twice fired home from the edge of the area.
"We had the better chances and played well, but we just didn't have that bit of luck we needed," lamented Sociedad boss Jagoba Arrasate.
However, despite the task now facing his side to qualify from a group that also includes Manchester United and Bayer Leverkusen, Arrasate insisted they will try to make amends when they travel to Germany in two weeks time.
"When you play in the Champions League this type of thing can happen but we are not going to give up after one game.
"We know we were going to have an exciting season but also a demanding one and by the time the Leverkusen game comes around we will be ready for it."
Sociedad had only been beaten once at home since last November and impressed mightily in thumping Lyon 4-0 on aggregate to qualify via the play-offs last month.
And it was the hosts that started this Group A clash on the front foot as Antoine Griezmann had an early effort parried by Shakhtar keeper Andriy Pyatov before only an excellent saving challenge by Olexandr Kucher prevented Carlos Vela from opening the scoring.
The home fans and players were left furious at Romanian referee Ovidiu Hategan as he only awarded a free-kick outside the area when Srna brought down Prieto despite the offence clearly taking place within the box.
Pyatov made a smart stop to deny Haris Seferovic from a narrow angle as the second half started just as the first had ended.
However, the visitors began to look more dangerous on the break as the half developed and, after Taison rightly had a goal ruled out for offside, Teixeira put Shakhtar in front when his low drive from the edge of the area went straight through Claudio Bravo in the Real goal on 65 minutes.
Real responded positively to going behind as Arrasate introduced last season's top-scorer Imanol Agirretxe from the bench.
And his side came within inches of an equaliser when Mikel Gonzalez saw his headed effort come off the crossbar on 77 minutes.
Shakhtar, though, were thriving on the counter as the hosts desperately pushed bodies forward in search of an equaliser, and Teixeira killed the game off three minutes from time when he cut inside and fired a magnificent effort into the bottom corner that left Bravo with no chance.