The Czech side thought they had salvaged a draw in Turkey last week, but they conceded a stoppage-time goal to trail ahead of the return leg.
Match preview
Sparta Prague, narrowly edged out by Rangers for top spot in their Europa League group, now face a tough test to stay in the competition after a dramatic first leg against Galatasaray.
The Czech side looked to have secured a valuable draw, only to be sunk by a stoppage-time winner.
Kerem Demirbay gave Gala the lead before Angelo Preciado levelled early in the second half. Dries Mertens restored the Turkish side's advantage on the hour mark, but their joy was short-lived as Victor Nelsson's red card swung the momentum back towards Sparta.
Brian Priske's men capitalised quickly, with Jan Kuchta finding the net for the second time. However, their numerical advantage was quickly nullified by Matej Rynes's dismissal.
With the game seemingly heading for a draw, Icardi struck a decisive blow deep into stoppage time to hand Gala the upper hand.
On the domestic front, Sparta maintained their lead at the top of the Czech First League with a 2-1 win over Liberec. They now turn their focus back to Europe, needing a turnaround at home to progress.
Meanwhile, Galatasaray will be aiming to extend their winning run to 11 matches across all competitions.
Okan Buruk's side followed their first-leg win over Sparta with a comfortable 3-0 victory over Ankaragucu to stay top of the Turkish Super Lig.
However, the Lions will be cautious of the threat Sparta carries especially as their away form in Europe has been patchy, losing two of their three games on the road.
With their tendency to both score and concede in most European fixtures this season, it remains to be seen whether this trend will continue and benefit them in Prague.
Sparta Prague Europa League form:
L
D
L
W
W
L
Sparta Prague form (all competitions):
W
W
W
W
L
W
Galatasaray Europa League form:
W
Galatasaray form (all competitions):
W
W
W
W
W
W
Team News
For Sparta Prague, Rynes will miss the game after he was sent off in the first leg.
Ladislav Krejci and Veljko Birmancevic will also miss Thursday's clash due to accumulated yellow cards.
Kuchta did not play from the start over the weekend, but should return to the starting XI against Gala.
Galatasaray will be without winter signing Serge Aurier, who is struggling with a back injury.
Tanguy Ndombele and Kaan Ayhan are also sidelined with muscle injuries that will keep them out until early March.
Hakim Ziyech may also miss the clash as he is still recovering from a thigh injury, while Nelsson is out due to the red card he received in the first leg.
Sparta Prague possible starting lineup:
Vindahl; Vitik, Vydra, Panak; Preciado, Kairinen, Laci, Zeleny; Karabec, Kuchta, Olatunji
Galatasaray possible starting lineup:
Muslera; Ayhan, Sanchez, Bardakci, Kutlu; Demirbay, Torreira; Yilmaz, Mertens, Zaha; Icardi
We say: Sparta Prague 2-2 Galatasaray
Having found the net twice against Galatasaray last week, Sparta Prague will fancy their chances here. However, we think the visitors will do enough not to lose this match and eventually go through on aggregate.