The Germans, with World Cup winner Matthias Ginter and Champions League-winning keeper Marc-Andre ter Stegen in their lineup, were swept aside.
To add to their misery Leonardo Bittencourt was sent off in the 75th minute for a second bookable offence.
Portugal captain Sergio Oliveira hit the post after 15 minutes but Bernardo Silva fared better in the 24th when he charged into the box and fired home.
Ricardo doubled the lead 11 minutes later, turning the ball in at the far post as the powerful William Carvalho, on the transfer wish-list of several top European clubs, controlled the midfield area.
Ivan Cavaleiro made it 3-0 on the stroke of halftime and Portugal scored again a minute after the restart when a deflected effort from Joao Mario sent Ter Stegen the wrong way.
Ricardo Horta completed the rout in the 71st minute, tapping in undisturbed from close range as the Germans were again caught napping.
The second semi-final in Prague was between Denmark and a hard-working Sweden side who qualified from their group at the expense of England and Italy.
The Swedes took the lead against the run of play in the 23rd minute, John Guidetti converting a penalty after strike partner Isaac Kiese-Thelin was fouled.
Three minutes later Guidetti turned provider, setting up Simon Tibbling for the second after a quick break down the left.
Despite their early goals it was the defensive effort of the Swedes that was most impressive and they were organised and energetic in their tackling and harrying.
Uffe Bech pulled a goal back for Denmark in the 63rd minute, scoring after the opposition fluffed two clearances in the box.
The Danes then launched an onslaught but the Swedes exploited the space behind to hit them twice on the break, two late goals from Robin Quaison and Oscar Hiljemark sealing an emphatic win.
Portugal and Sweden, who shared a 1-1 draw in the group stage, now meet again in Prague on Tuesday.
(Reporting by Karolos Grohmann and Philip O'Connor,; editing by Toby Davis and Tony Jimenez)
