Robert Lewandowski scored twice as reigning champions Bayern came from behind to beat Mainz 3-1 away from home.
Afterwards, Rummenigge heaped praise on head coach Carlo Ancelotti and Co, saying: "We were very dominant today, especially in the first half.
"The victory was absolutely deserved. Carlo Ancelotti and his team laid down a marker today.
"If we play well and use today's performance as a benchmark we have a good chance of winning the German championship title."
Dutch attacker Robben celebrated his 150th Bundesliga appearance in style, putting Bayern ahead in the 21st minute after setting up Lewandowski for the equaliser 13 minutes earlier at Opel Arena.
"We've not played as well as we did in the first half for some weeks. It's great fun for the players," Robben said.
"Our movement was good and we came up with lots of surprises, these surprise moments we've lacked in the last few weeks. We played really, really well in the first half and should have scored more goals. In the second half we should have simply kept going, maintained the pace and moved the ball quickly.
"But we eased off, we lacked the pace and maybe also the movement. If we'd made it three, it would have been over."
Thomas Muller added: "After the early shock we were fluid in attack and controlled the game well in the first half. The intensity was right, even if we lost possession a little too often in the second half, which caused a few problems. It was fun today."