Goals from Phillip Lahm (39), Sami Khedira (61), Miroslav Klose (68) and Marco Reus (74) were enough to complete an overwhelming win with Georgios Samaras scoring an unlikely equaliser for Greece early in the second period.
Dimitris Salpingidis netted a penalty for Greece on 89 minutes after Jerome Boateng was harshly penalised for a handball, but Germany were convincing winners on the night.
Loew caused some consternation before the match when he opted to bring in Andre Schuerrle, Reus and Klose for three of his more established players - certainly at these finals in Poland and Ukraine - of Lukas Podolski, Thomas Mueller and Mario Gomez, men who had helped them reached the last eight with wins over Portugal, the Netherlands and Denmark in the group stages.
It mattered little as Germany camped out in the opposition half for large swathes of the match. They could and should have won by a greater margin on their way to a 15th straight win - a record for the German national side.
Germany will face England or Italy in the second semi-final in Warsaw on Thursday. They will be difficult to hold in this mood.
Watched by their country's chancellor Angela Merkel, Germany basked in 76 percent of possession and totted up 26 shots at goal compared to only ten from Greece.
Germany headed for half-time holding a one-goal lead when captain Philipp Lahm bounded beyond Sotiris Ninis to sink a volley beyond Greece goalkeeper Michail Sifakis from 20 yards out on 39 minutes.
Schuerrle had the ball in the net in four minutes, but the goal was disallowed for offside after Sifakis had spilled Khedira's shot. The chances came and went for Germany as Mesut Ozil, Reus, Khedira and Schuerrle all had opportunities to put the game beyond the besieged Greece side, whose policy of defend deep and counter attack was doomed to failure by the technique and ongoing energy levels of Germany.
It was difficult to believe a match could be more one-sided than Portugal's 1-0 win over Czech Republic on Thursday, but they certainly managed it as Greece seemed to be playing a nine-man back line at times.
Greece somehow drew level with their best move of the match and the tournament as Samaras forced the ball under Manuel Neuer from a lovely ball across goal by Salpingidis on 55 minutes. It was a only a brief reprieve as it became clear Greece lacked the quality to emulate their rise to the trophy at Euro 2004.
Indeed, Samaras's goal only seemed to further aggravate Germany who reclaimed the lead when Khedira thumped Jerome Boateng's cross into the net from 12 yards to establish a 2-1 lead before the creaking Sifakis missed the outstanding Ozil's free-kick as Klose rose above Kyriakos Papadopoulos to head his 64th goal in his 12oth appearance for his country.
He is only four goals adrift of Gerd Mueller's record of 68 for Germany in 62 matches for West Germany. Reus clubbed a volley into the vacant net with 16 minutes left after Sifakis had smothered a Klose effort with Ozil again leading Greece a merry dance in the middle of the park.
Greece scored their second of the night when Salpingidis sent the underworked Neuer the wrong way from the penalty spot after Boateng was deemed to have intentionally blocked Vasilis Torosidis's shot with his hand.
It enabled Greece to score a second goal on the night yet the scoreline flattered them.
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