Replacing Mario Gomez, the tournament's joint top scorer, with Miroslav Klose and omitting the experienced Lukas Podolski and Thomas Muller in favour of the relatively green Marco Reus and Andre Schurrle may have raised eyebrows in some quarters.
But Klose responded with his 64th international goal on his 120th appearance, while Schuerrle and especially Reus gave the Greek defence a torrid time, the latter crowning his seventh cap with a fine volleyed goal.
Low's surprise starting line-up for the quarter-final at Gdansk's PGE Arena underlined the depth in the German squad and it was an accomplished performance from a strong, physical team who will pose a stern test for Italy or England in the semi-finals.
"I had a feeling after three wins that we had to make some changes to breathe some fresh life into the team," Low told reporters.
"The time was ripe to do something different. I think Miro and the others did it very well."
Klose, now four short of Gerd Muller's German scoring record of 68, added: "It's amazing if you look at how many good players can come off the bench and play.
"We can now relax and watch the England-Italy match and see who we're going to be playing against."
A pass completion rate of 79 percent is well below what Ozil would normally achieve in La Liga, although he did provide the assist from a free-kick for Klose's header.
The performance of defender Jerome Boateng on his return from suspension may also have given Low food for thought after he let Giorgos Samaras nip in front of him to score Greece's equaliser and gave away the late penalty for handball for their second.
"We made it unnecessarily difficult for ourselves," said captain Philipp Lahm.
"We were too slow at times and made too many easy mistakes," added the 28-year-old, who put Germany in front with a swerving, long-range drive just before halftime.
"But the important thing is that we're in the semi finals. I think we're finding our rhythm more each match."
