Ricardo Quaresma's header after skipper Ronaldo's shot was deflected with extra time running out saw Portugal defeat Croatia 1-0 and set up a last eight clash against Poland.
Bayern Munich star Lewandowski again failed to score but Poland beat Switzerland 5-4 in a penalty shootout after they were deadlocked 1-1 at 120 minutes.
Wales's Bale hit the 75th-minute pinpoint cross that Northern Ireland's Gareth McAuley turned into his own net in the only goal of their game Saturday. Wales now play the winner of Sunday's game between Hungary and Belgium.
Northern Ireland closed down Bale for so long. But Wales have reached the last eight of a major tournament for the first time since the 1958 World Cup.
"What can I say? We knew it was going to be an ugly match," Bale said.
"Northern Ireland made it difficult to play. There was not much space up front. You can't ask for any more. It's incredible."
- Euro roulette -
Northern Ireland manager Michael O'Neill said his team deserved more after keeping Bale in check for so long.
"I felt it was a very tight game and I felt we had the better of it to be honest," said O'Neill. "It was a very, very cruel was to lose the game. I didn't think we deserved to lose."
In Lens, a Croatia team -- led by another Real Madrid star Luka Modric -- 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 Euro history in which neither team managed a shot on target during the regulation 90 minutes.
Portugal then snatched their first victory of the
tournament at the death as Quaresma was perfectly positioned to head in after Ronaldo's low shot was parried away by goalkeeper Danijel Subasic.
"We cannot say football is fair, we had many chances, we dominated for the whole match, so it was not a psychological problem," said Croatia coach Ante Cacic. "The best team doesn't always win and that happened tonight."
He did name Ronaldo's team, however, as favourites to reach the July 10 final in Paris.
With Lewandowski drawing another Euro blank at Saint-Etienne's Stade Geoffrey Guichard, Jakub Blaszczykowski scored the crucial opening goal for Poland but Switzerland drew level in spectacular style through Shaqiri.
The match went to a penalty shootout but Arsenal-bound Granit Xhaka's wild and wide spot-kick cost the Swiss dear. The Poles went a perfect five from five from the spot.
"POL!!! Final 8!!!" tweeted "Gladiator" star Russell Crowe, who has taken this rugged Polish team and swashbuckling winger Blaszczykowski to his heart.
Swiss coach Vladimir Petkovic was another who felt his side had lost despite dominating. "Penalties are like roulette," he moaned.
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.
"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.
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