The Portuguese club continue their impressive European campaign, and have now booked a semi-final showdown against Marcelo Bielsa's Athletic Bilbao
A first-half goal from Ricky van Wolfswinkel put the visitors in the lead, before Jonatan Cristaldo restored parity shortly after the break. Metalist then spurred a chance to take the lead as Cleiton Xavier missed a penalty, and it proved costly, as the Portuguese side held on to progress.
The match started off at a fast pace, with Metalist in command of proceedings, as the Ukrainians went in search for the goal which could send them into the next round.
However, it was not until the 27th minute that a genuine chance was created. Cleiton Xavier picked up the ball inside the Sporting box and attempted a volley from a tight angle, but Rui Patricio tipped the ball round the post.
Four minutes later, it was Taison's turn to wreak havoc as he picked up possession 25 yards out and moved past two defenders, but his low shot was denied by Patricio's right leg.
Metalist were in control of the match, but just before half-time they were penalised for their inability to convert their superiority into goals.
Diego Capel, down the left flank, cut inside before delivering a cross to the far post. Ricky van Wolfswinkel rose between two defenders to head the ball past Olexandr Goryainov, and give Sporting a clear advantage.
The second half began with Metalist once again the livelier of the two sides, and the hosts equalised in the 57th minute through Jonatan Cristaldo, who sent a low shot through the legs of Patricio after being assisted by Marko Devic.
The Ukrainians wasted a clear chance to score just seven minutes later, when they were awarded a penalty after Devic was felled by Emiliano Insua inside the box. Cleiton Xavier failed to convert from the spot as his low shot was stopped by Patricio's left leg.
Metalist continued to push for the goal they needed to send the match to extra-time, but they could not find that elusive strike.
With this result, Sporting are through to the last four of the competition, where they will tackle Athletic Bilbao.