The home side looked on course to take a comfortable lead into the second leg of the quarter-final when Marat Izmailov and Emiliano Insua put them 2-0 in front at Estadio Jose Alvalade.
However, Cleiton Xavier converted a 90th-minute spot-kick to give the Ukrainian side a vital away goal and firm foothold in the tie.
After a quiet opening, Sporting created the first real opening as defender Xandao fired wide from the edge of the area with 12 minutes on the clock.
The visitors soon got into the contest however and Jonathan Cristaldo's long-range shot was blocked by Anderson Polga before Taison drilled a free-kick wide from even further out.
At the other end, Izmailov saw his shot blocked by Marco Torsiglieri just seconds before Daniel Carrico's shot was comfortably held by Oleksandr Goryainov.
It took Sporting just five minutes of the second half to break the deadlock as the impressive Izmailov converted Diego Capel's cross from six yards.
And a minute later it was almost 2-0 as Matias Fernandez saw his long-range free-kick tipped over by Goryainov.
But the home fans among the crowd of 40,512 did not have to wait too long for the second goal, with Insua hammering home a 25-yard drive into the bottom corner in the 64th minute.
To the visitors' credit they refused to throw in the towel and Taison's shot was tipped round the post by Rui Patricio before the goalkeeper was again called into action to block Jose Sosa's 12-yard effort.
But just when it looked like Patricio would be Sporting's hero, the goalkeeper brought down Marko Devic after saving an initial shot from substitute Marlos to concede a penalty.
Patricio was booked for his troubles and was then powerless to prevent Cleiton hammering in the spot-kick to leave the tie finely poised.