The 1-0 win in a game which only burst into life in the final minutes in Lens earned Ronaldo’s side a quarter-final meeting with Poland in Marseille on Thursday.
After scraping through their group without a single victory, Portugal’s star power finally shone through just as the match seemed to be heading for penalties.
“The best team doesn’t always win and that happened tonight,” Croatia coach Ante Cacic said.
Poland progressed to the quarter-finals of a Euros for the first time by beating Switzerland in a penalty shootout in Saint-Etienne, delighting celebrity fan Russell Crowe.
Arsenal-bound Granit Xhaka’s wild and wide spot kick cost the Swiss dear as the Poles were a perfect five from five from the spot.
“POL!!! Final 8!!!” tweeted “Gladiator” star Crowe, who has taken this rugged Polish team and swashbuckling winger Jakob Blaszczykowski to his heart.
– Post-Brexit clash –
Ronaldo’s Real Madrid teammate Gareth Bale failed to score for Wales in a post-Brexit all-British clash against Northern Ireland, but his cross was deflected into his own net by Gareth McAuley for the decisive goal.
The 1-0 win at a raucous Parc des Princes in Paris was probably the dullest game of the tournament so far, but Bale said Wales could not care less as they reached the last eight of a major tournament for the first time since the 1958 World cup.
“It’s an ugly win but who cares,” said Bale.
“You can’t ask for any more. It’s incredible.”
Wales will face Belgium or Hungary in Lille on Friday for a place in the semi-finals.
In Lens, a Croatia team that has played some of the most attractive football of the finals failed to find a way past the Portuguese defence.
Ronaldo was muzzled for the vast majority of a dull encounter that became the first match in Euros history in which neither team managed a shot on target during the regulation 90 minutes.
Domagoj Vida had a golden chance to settle the game for Croatia but headed wide after Portuguese goalkeeper Rui Patricio failed to collect a corner.
However, Patricio saved his country seconds later when he turned Ivan Perisic’s header onto the post.
Portugal then snatched their first victory of the tournament at the death as Quaresma was perfectly positioned to head in after Subasic saved Ronaldo’s low shot.
A jubilant Quaresma sprinted to the corner flag where he disappeared under a heap of celebrating teammates.
– Goal of the tournament –
At Saint-Etienne’s Stade Geoffrey Guichard, Blaszczykowski opened the scoring for Poland but Switzerland drew level in spectacular style with Xherdan Shaqiri’s bicycle kick, a potential goal of the tournament.
When the teams could not be separated in extra-time, it was Xhaka who cracked first in the penalty shootout, blasting well wide with Switzerland’s second spot kick.
The Poles scored all five penalties, rounded off by Grzegorz Krychowiak’s emphatic finish which put his nation into the quarter-finals of a major tournament for the first time since the 1982 World Cup.
“I’m delighted, it was a historic moment for us, because we are in the top eight in Europe,” Blaszczykowski said.
After Crowe added his congratulations, European Union president Donald Tusk, who is Polish, shared his nation’s joy, tweeting: “I have waited for this for so many years! My God I am happy!”
France’s clash with the Republic of Ireland on Sunday, which evokes memories of Thierry Henry’s infamous handball in a 2009 World Cup playoff, was given further edge with a row over tickets.
Ireland coach Martin O’Neill is angry because Irish fans received just 4,500 tickets for the match in the 59,000-capacity Stade de Lyon.
“It’s totally disproportionate for a stadium of this size,” O’Neill complained.
“For us, or any team that was going to be playing in the round of 16 here, to be allocated less that 5,000 tickets is, I think, pretty unfair, honestly.”