Goals from Ismaila Sarr, Daichi Kamada and Jorgen Strand Larsen in Poland put the Eagles in command of the tie despite a spirited performance from the Ukrainian league leaders.
Shakhtar have remained remarkably competitive in European football despite their long exile from Ukraine due to the ongoing conflict with Russia.
But the vast difference in resources between the sides showed as Strand Larsen, who joined Palace for a club record £48 million ($65 million) in February, came off the bench to give last season’s FA Cup winners a two-goal cushion late on.
Palace got off to a dream start as they took the lead after just 21 seconds.
Jean-Philippe Mateta and Yeremy Pino combined nearly before the former played in Sarr to fire home his 18th goal of the season, eight of which have come in the Conference League.
But Arda Turan’s side penned back their Premier League opponents for the remainder of the first half and got their reward early in the second period.
Oleh Ocheretko slotted home the equaliser from close range after Palace failed to clear a corner.
However, the goal sparked Oliver Glasner’s men back into life.
Dmytro Riznyk produced a brilliant double save to deny Sarr and Mateta before the French striker hit the post from a long throw.
Shakhtar did not heed the warning as from Chris Richards’ next throw into the box, the ball broke kindly for Kamada to drill under Riznyk.
In their quest for an equaliser, Shakhtar were then picked off on the counter-attack.
Kamada picked out Strand Larsen, who coolly cut inside and chipped the onrushing Riznyk for his fourth goal since joining from Wolves.
Prior to shocking Manchester City in last season’s FA Cup final, Palace had never won a major trophy in their history.
Now they are the favourites to add a second in 12 months with Rayo Vallecano or Strasbourg awaiting the winners in the final in Leipzig on May 27.
Rayo edged the first leg of the other semi-final 1-0 in Spain.
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