Toni Kroos was also on target to leave the world champions on six points from two games in Group C, alongside Azerbaijan after they beat Norway 1-0 in Baku with an early goal by Maksim Medvedev, and firmly on course for the finals in Russia in 2018.
The Czechs, who have one point, won 3-0 on their last visit to Germany in 2007 in the early days of coach Joachim Loew's long reign but never threatened a repeat.
"I'm very satisfied, we had control of the game for the whole time," said Loew.
"We built up our moves very well from the back. We put together some great combinations and didn't give our opponents any chance."
Germany broke the deadlock after 13 minutes when Mario Goetze burst down the left, his pass into the area was touched on by Mesut Ozil and Mueller scored with a shot which took a slight deflection off a defender.
Germany, who beat Norway by the same score in their opening qualifier last month, continued to carve open the Czech defence with neat interchanges between Mueller, Ozil, Julian Draxler and Goetze who was playing as a false number nine.
Draxler pinged a shot just wide after Goetze pulled the ball back to him, Mueller saw a low drive turned away by Czech goalkeeper Tomas Vaclik, then Goetze dinked the ball wide after a one-two with Mueller.
Kroos doubled Germany's lead four minutes after the restart when he got in front of his marker and placed a sidefooted shot past Vaclik after Joshua Kimmich rolled the ball across the edge of the area.
Germany goalkeeper Manuel Neuer made his first save in the 63rd minute when he parried Borek Dockal's powerful effort and the home team struck again two minutes later, Mueller turning in Jonas Hector's low cross at the near post.
"We could have scored more goals, we have played a very convincing game," said Mueller. "I'm happy to have scored two."
(Writing by Brian Homewood; Editing by Tony Jimenez)
