Leading 2-1 from the first leg in Portugal, Sporting extended their lead through Ricky van Wolfswinkel before Jonathan Cristaldo equalised early in the second half to pile the pressure on the visitors.
But Metalist blew their big chance of levelling on aggregate in the 63rd minute when Alexandre Xandao fouled Marko Devic in the box, and Xavier rattled his resulting spot-kick at the legs of Sporting goalkeeper Rui Patricio.
The Ukrainians had pushed forward from the start, with Edmar forcing a save out of Patricio in the third minute with a close-range header from a free-kick from the busy Xavier.
After the visitors responded by forcing a series of corners, Metalist again went on the offensive and came close to opening the scoring in the 12th minute when Cristaldo headed over from six yards.
Metalist were creating most of the chances and Rui Patricio did well to maintain Sporting's slender aggregate lead in the 29th minute when he tipped over an 18-yard shot from Xavier.
Freda Taison shot at the keeper's feet and Cristian Villagra fired over the bar from 12 yards before Sporting fashioned a rare shooting chance with Marat Izmailov hitting a shot over from long range.
With Sporting nudging back into the match, Van Wolfswinkel forced a 39th-minute save out of Oleksandr Goryainov, but Metalist came close again two minutes later when Patricio saved brilliantly to deny Xavier.
Out of nowhere, Sporting grabbed the opener in the last minute of the first half when Van Wolfswinkel headed home a cross by Diego Capel, extending the Portuguese side's aggregate lead.
Needing to score at least twice, Metalist made a good start to the second half with Cristaldo having a shot blocked in the box in the 48th minute and a dangerous Xavier free-kick booted clear by Xandao.
Matias Fernandez missed with a long-range effort which would have sealed it for the visitors in the 55th minute, and Metalist responded by equalising four minutes later when Cristaldo fired home from Devic's header down.
Metalist looked like pulling their way back into the match but after their penalty miss it was Sporting who regained control, and Metalist could summon no more clear-cut chances as the minutes ticked by.