Barca, eight points clear at the top of La Liga and due to face Real in the Spanish Cup final on Wednesday 20 April, are bidding for a repeat of the Treble they achieved in coach Pep Guardiola's first season two years ago.
They completed the formalities in Donetsk after a scintillating performance at the Camp Nou six days ago that had all but secured their progression into the last four for a fourth successive season.
As in the first leg, they had to survive some early Shakhtar pressure - but the Ukrainian side's inability to take advantage of their initial supremacy once again cost them dearly.
Shakhtar coach Mircea Lucescu rues a missed early opportunity
Roared on by a partisan crowd, many of whom had seen Shakhtar lose at the Donbass Arena - their home since September 2009 - for the first time against Obolon Kiev at the weekend, the hosts began with a real purpose and unsettled their illustrious opponents.
Two of Shakhtar's Brazilian front four, Jadson and Costa, combined superbly only for Costa's shot to draw a fine save from Valdes, who was called into action again shortly afterwards when he saved Jadson's 20-yard effort after an exchange of passes with Costa.
Jadson then directed a Vasyl Kobin cross from the right straight at Valdes, before Barca, prompted from midfield by Xavi and with Messi dropping deep to try and have a bigger say on the game, suddenly moved through the gears.
Messi fired a warning shot into the midriff of Pyatov after finding some space outside the box and then, after Adriano's shot was cleared off the line by Yaroslav Rakitskiy, Messi wriggled clear of the defence only to tamely chip into the arms of the Shakhtar keeper.
The Argentine was beginning to enjoy himself, however - and just before half-time he got the goal that finished Shakhtar off and earned himself a new Spanish goalscoring record in the process.
He fastened on to an Alves ball from the right, taking a touch and slotting low past Pyatov's outstretched left hand as he went past the goal tallies of Real Madrid legend Ferenc Puskas in 1959-60, Barca's Brazilian Ronaldo in 1996-97 and Messi himself last season.
With the away goal in the bag and any remote chance of a Shakhtar comeback snuffed out, Barca turned on the style in the second half, moving the ball around the park with their customary sparkle.
A mazy Messi run took him past two Shakhtar defenders and opened up a pass to Afellay on the left but Pyatov produced a wonderful save to keep out the Dutchman's curling effort and then Alves screamed the rebound wide from 20 yards.
Shakhtar's fans refused to be downcast as they urged their team on to try and get on the scoresheet at least but Valdes and Barca would not let them past, the keeper sticking his left hand out to brilliantly deny Henrik Mkhitaryan.
With a potential four 'El Clasico' games against Real coming up in the next few weeks and three trophies on the line, Guardiola's side are warming up for the crucial part of the season in ominously impressive fashion.
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