Edinson Cavani squandered a glorious chance midway through the first half, while Diego Godin was guilty of similar profligacy after the interval as Peru hardly tested their opponents at the other end.
Uruguay, who also had a goal disallowed in the first half, twice fell foul of tight offside decisions after Godin's miss – both Cavani and Suarez denied by the flag and subsequent VAR checks.
And Uruguay's misfortune continued in the shoot-out – Pedro Gallese making a fantastic save from Suarez's opening penalty, with Edison Flores later stepping up to clinch Peru's place in the last four, where defending champions Chile await.
¡CLASIFICAMOOOS!— Selección Peruana (@SeleccionPeru) June 29, 2019
Nuestra @SeleccionPeru venció 5-4 a @Uruguay en definición por penales tras igualar 0-0 y accedió a las semifinales de la @CopaAmerica.
¡Unidos somos más fuertes, sigamos alentando y siendo #LaMejorHinchadaDelMundo!
Siempre #ArribaPerú pic.twitter.com/dKusqEC6qt
Suarez's deflected shot created a superb opportunity for his strike partner in the 23rd minute, but Cavani somehow blazed over an open goal from six yards out.
Giorgian de Arrascaeta then thought he had put Uruguay ahead, only for his strike to be disallowed for offside.
Godin lashed wildly over from close range as Uruguay kept up the pressure – the offside flag then coming to Peru's rescue again when Cavani's goal was ruled out just before the hour.
Uruguay were denied for a third time when Suarez's tap-in was chalked off 12 minutes later, as penalties were required for the third time in four quarter-final ties.
And despite failing to test Fernando Muslera at all during the match, 2015 semi-finalists Peru made their good luck count, converting five excellent spot-kicks to secure progression after Suarez had seen his effort brilliantly saved by Gallese.
What does it mean? Defending champions Chile have little to fear
While Chile were less than convincing against Colombia, Peru's backs-to-the-wall display should not have struck fear into the two-time defending Copa America champions.
Chile should be confident that – with a rejuvenated Alexis Sanchez in their ranks – they have the quality to make it to a third successive final as long as they do not replicate Uruguay's wasteful finishing.
Gallese proves Peru's shoot-out hero
Suarez's penalty was struck with plenty of power, but Gallese was brave, diving to his right and making himself big to make the stop which set his team-mates up to secure Peru's progression.
Miss of the tournament from Cavani?
Cavani could well have avoided the drama of penalties – and ultimately spare Suarez's blushes – had he converted an easy chance in the first half. The ball fell to him on a plate, but despite having the entire goal to aim at, he managed to slice it over.
Key Opta Facts:
- Peru have reached the Copa America semi-finals for the third time in the last four tournaments, after managing to do so in only one of the previous seven campaigns (1997).
- They have also won a Copa America penalty shoot-out for the first time, after losing against Mexico in 1999 and against Colombia in 2016.
- Uruguay have now been involved in the joint-most penalty shoot-outs (nine) in Copa America history (W4 L5).
- Peru are the first team to attempt no shots on target in a game during this tournament; they had three total shots against Uruguay, all of them off-target.
- Uruguay took part in the three first halves of the 2019 Copa America with the lowest passing accuracy (73.1% Uruguay v Ecuador; 73.7% Uruguay v Peru; 75% Uruguay v Japan).