Kyriakos Papadopoulos had headed the visitors into a deserved half-time lead yesterday as Barca struggled to open up the Germans without Messi's magic touch.
However, despite also losing Andres Iniesta to a hamstring injury, Suarez turned the game around in the final 10 minutes as Sergi Roberto tapped home the rebound after the Uruguayan's initial effort had been saved.
And the former Liverpool striker thumped home a stunning effort to hand Barca a hard-fought three points, two minutes later.
"We believed in ourselves until the end," Suarez told beIN Sports.
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"We couldn't play great football, but we had to win the game. We had to show we are the champions."
Messi was in attendance at the Camp Nou, but his teammates made a shaky start without him on the field as former Real Madrid striker Javier Hernandez forced Marc-Andre ter Stegen into a smart save at his near post inside two minutes.
Ivan Rakitic had Barca's first effort on target, but the Croatian placed his header too close to Bernd Leno.