Robben scored in the second and 30th minutes as the hosts kept up their blistering pace at the top of the table.
Victory completed a fine eight-day spell for Bayern, who started it with a 3-0 win at Borussia Dortmund and also won at CSKA Moscow in the Champions League in midweek.
"I am happy," Guardiola said on the Bayern website. "Robben is very important for us and gets a lot of goals. You saw that Braunschweig also had chances. The Bundesliga is a very hard league."
Robben was pleased with the team's response just four days after the trip to Moscow.
"It was a hard match in Moscow, also with the whole journey," he said. "When you then come back home and play on this excellent pitch, that's fun."