Ronaldo headed home a cross from Joao Moutinho 11 minutes from the end to set up a possible semi-final against either world champions Spain or France.
It was just reward after another starring performance from the Real Madrid man against opponents who failed to register a single shot on target and were hindered by the absence of injured playmaker Tomas Rosicky.
The Czechs began brightly mainly attacking from the flanks but failed to penetrate the Portuguese back four. However, on the other end of the field, the Czechs goal-keeper Petr Cech was forced to save free kicks, long shots and also block dangerous crosses. Former teammates in Manchester United, Ronaldo and Nani fired in shots relentlessly, but the Chelsea stopper Cech made four brilliant saves.
"We had the quality to pass into the semi-finals," said Ronaldo. "We are happy but know the next match will be difficult but the team is very mature and we are ready. "There are big smiles and good music all round us!"
Portuguese winger Nani, who also had an outstanding game, said that the victory while long in coming was deserved. "We played really well, we were stylish on the pitch and it was a great team effort," said the Manchester United star. "Now its going to be more difficult in each game but we are very confident. "I had a couple of chances which went close but that's how it is in football, Ronaldo as well went close but he hit the target in the end."
Czech coach Michal Bilek admitted graciously that his side had been outclassed. "The Portuguese were the best side, much stronger in the footballing sense," said the 47-year-old. "Their attack is very strong. Petr Cech pulled off some stunning saves to keep us in the game.
"We had wanted to play with a solid defence and rely on the counter-attack, but we started to run out of energy during the second-half." As is so often the case in knock-out matches in big tournaments, the first half was a cagey affair.