Barca, champions in 1992, 2006 and 2009, will now meet either bitter rivals Real Madrid or Tottenham in the last four after Messi made the difference just two minutes before the break to reach the semi-finals for the fourth successive season.
"This fourth consecutive qualification for the semi-finals is a huge achievement," said Barca coach Pep Guardiola.
"Barcelona have never done this before. This is a huge pleasure."
His Shakhtar Donetsk counterpart Mircea Lucescu complimented Barcelona on their win and said he hoped they would go on and win the trophy.
"This was a spectacular match; in spite of the large number of players missing from our side, we had more chances than any team should normally have against Barcelona.
"This was a great opportunity to play against Barca, and this will be a useful experience for our young team for next season," added the veteran Romanian, whose side were praised by Guardiola.
Messi moved to the head of the goascoring charts in this season's tournament by breaking the deadlock at the Donbass Arena, firing in low and left-footed.
A deft flick almost saw the Argentine double the advantage on the night to give Shakhtar, seeking to regroup after a weekend home loss to Obolon, even more of a mountain to climb after a 5-1 romp for the Catalan club in the Nou Camp.
Yet the Ukrainians had enjoyed the better of the opening exchanges despite being without captain Dario Srna owing to an injured thigh while Olexandr Kucher and former Barca defender Dmytro Chygrynskiy were also on the casualty list and left back Razvan Rat was suspended.
However, Barca weathered the early storm and Messi's riposte deflated their hosts.
Barca, beaten in the semis last season by eventual winners Inter Milan, themselves had to rejig their starting eleven as they targeted a likely semi-final with bitter rivals Real Madrid.
Guardiola drafted Thiago Alcantara, Andreu Fontas and Jonathan dos Santos into his squad with Eric Abidal, Carles Puyol and Bojan Krkic all injured, while midfield star Andres Iniesta missed out through suspension.
Dutch forward Ibrahim Afellay was handed a starting berth on the right flank in place of groin strain victim Pedro with David Villa and Messi spearheading matters in attack.
Barca were keen to avoid any further injury worries with this weekend bringing a key league clash against Real - whom they lead by eight points. Avoiding defeat in that game will leave Barca with a hand on the championship trophy - but Guardiola will be under even more pressure to ensure that Real are sent packing in the semis.
The latter first have to dispose of Tottenham in Wednesday's semi-final return having triumphed 4-0 in Madrid.
Lucescu surprisingly left Brazilian midfielder Fernandinho off his starting selection but did pick Luiz Adriano up front, and his side fought gamely after the break but were unable to force their way back into the tie as Barca cantered on.
Fernandinho did get 15 minutes to try his luck but it was Henrik Mkhitaryan who came closest to giving the home crowd something to shout when it took a superlative save from Victor Valdes to keep out his 74th-minute goalbound effort.
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