The first-half was devoid of much action of note with the best chance falling to the head of Pepe but he failed to re-adjust his body and could only nod over the bar.
Croatia, so impressive last time out against Spain, had the lion’s share of possession but were unable to prise a clear-cut opening from a resolute Portugal defence.
It was much the same for the second-half but the best chance fell to another defender just after the hour mark.
However, Domagoj Vida could only glance Darijo Srna’s cross wide of the post, and the game went to extra-time.
With neither side able to assert any authority, it looked as though the game would go to penalties but with 117 minutes on the clock Quaresma followed up Cristiano Ronaldo’s saved effort to slot home and secure their spot in the next round.
Nani is only the 4th player to reach 100 games for Seleções de Portugal , after Fernando Couto, Luís Figo & Cristiano Ronaldo .
In other results, Poland reached the last eight of Euro 2016 after seeing off Switzerland in a penalty shootout, following a 1-1 draw in normal and extra time while Wales won the British battle against Northern Ireland one nil
FT Switzerland 1-1 Poland (Pen:4-5)
FT Wales 1-0 Northern Ireland