The Argentine superstar netted the only goal of the match as the Catalan giants produced a professional performance to seal the tie and book their place in the final four
Lionel Messi struck the only goal on the stroke of half-time to seal a comprehensive win over the two legs and set up a potential last-four meeting with fierce rivals Real Madrid.
Despite the seemingly impossible nature of the task facing the Ukrainian side, their followers packed into the stadium in hope that they could produce a miracle comeback.
Shakhtar's Brazilian front quartet started the better in front of their vibrant home support and should have taken the lead in the opening 10 minutes. Jadson slipped a sliderule pass into the path of Luiz Adriano, but the striker's turn and shot was saved by the strong wrist of Victor Valdes.
Visiting coach Pep Guardiola had opted to field a strong XI despite Real Madrid awaiting them in La Liga this weekend and the Catalan giants eventually played their way into the contest in their own inimitable style.
Messi tested Andriy Pyatov from long-range, while Ibrahim Afellay, who was offered a rare start, also warmed the shot stopper's gloves from outside the area.
Whatever fading aspirations Shakhtar held over performing the unthinkable were extinguished two minutes before the break, however, and it was Messi who made the difference.
Linking with Dani Alves on the right, the Argentine burst into the area and as the ball broke kindly into his path, he drilled his effort instinctively, low and into the corner out of the reach of Pyatov, for his ninth Champions League goal of the season. The stadium fell silent; the inevitable was now upon Mircea Lucescu's men.
Touch of class | Messi strikes to seal the tie for BarcelonaShakhtar were desperate to restore an element of pride in the second period, and having surrendered their two-and-a-half year unbeaten home record at the weekend, did not want to taste defeat again.
And yet it was Messi who tormented them once more. The Ballon d'Or winner slalomed through the centre of the pitch before laying in Afellay, but the Dutchman's curling shot was beaten to safety by Pyatov.
Lucescu threw Eduardo and Fernandinho into the action, and Mkhitaryan forced Valdes into a smart save, palming over the crossbar from 12 yards, but the hosts were destined not to make the breakthrough.
The 2009 European champions held on to secure their first away win in the knockout stages under Guardiola and kept their end of the bargain in terms of establishing a Clasico semi-final against the men from Madrid, who play Tottenham on Wednesday.
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