Palace will face two-time Conference League runners-up Fiorentina in the last eight after the Italian club won 2-1 at Rakow Czestochowa in Poland, completing a 4-2 aggregate success.
The Eagles have endured a stop-start season, hit by the departure of centre-back Marc Guehi to Manchester City and the announcement that manager Oliver Glasner will leave at the end of the campaign.
But the English club remain in contention to add to their first ever major trophy, the FA Cup won last season, in their maiden European campaign.
Palace named a strong side for the last-16 second leg after two wins in four matches in recent weeks eased their Premier League relegation fears.
The visitors took a 13th-minute lead when Sarr was played in behind by Adam Wharton’s deflected pass.
The Senegal winger kept his cool to round home goalkeeper Zlatan Alomerovic, who had advanced out of his area, and roll the ball into an empty net.
Sarr thought he had doubled the lead shortly afterwards but was flagged offside.
Larnarca managed to stay in the tie despite prolonged Palace pressure, though, and levelled 18 minutes into the second half through Enric Saborit’s header.
The Spanish left-back was then sent off in the 73rd minute after receiving a second yellow card for a foul on Sarr, but the hosts held on to force extra time.
The Cypriots could not keep Palace at bay with 10 men until penalties, as Sarr fired home in the 99th minute from Daichi Kamada’s pullback after a short corner.
It was Palace who looked more likely to score the game’s fourth goal, as Sarr rattled the crossbar and then Jorgen Strand Larsen headed against the post, with the Dane and Jean-Philippe Mateta somehow contriving to fail put the rebound in between them.
Larnaca defender Petros Ioannou was dismissed late on for a foul on Mateta, but Palace still had to survive a nervy late set-piece to avoid a shoot-out.
Mainz saw off Czechs Sigma Olomouc 2-0 in Germany, winning by the same score on aggregate, to set up a quarter-final tie against either Strasbourg or Rijeka. (AFP)
Edited by Cecil Wong
