The Arsenal trio performed well in torrential conditions in Recife, with Mertesacker playing a key role in the only goal of the game.
It was his firm header in the 55th minute that was saved by Tim Howard, with the loose ball falling to Thomas Muller to stroke home.
Ozil was a threat going forward and came close to opening the scoring in the first half with a low shot that Howard did well to stop with his legs. The Arsenal playmaker was eventually replaced after 89 minutes.
Podolski was full of energy and running in the first half, but was taken off at the break and replaced by Miroslav Klose.
Germany will play Algeria in Porto Alegre on Monday.Copyright 2016 The Arsenal Football Club plc. Permission to use quotations from this article is granted subject to appropriate credit being given to www.arsenal.com as the source