Reus scored after 39 minutes and Mueller soon doubled their lead as the Germans, who had an erratic start to qualifiers last year and lost in Poland, were never threatened by their weaker opponents.
The win lifted Germany to 10 points from five games, as many as leaders Poland, who take on Ireland later on Sunday. Scotland are also on 10.
"A look at the table before the game was enough to see the urgency of the situation," Germany coach Joachim Loew told reporters. "We played a dynamic game, we then controlled it in the second half but did not have the same drive towards goal."
Loew said their conversion rate would need to improve after again spurning several good chances and hitting the woodwork twice.
"We again missed some good chances. We had good combinations but failed to score a third or fourth goal."
Georgia have had a tough start in Group D, recording four defeats and a win in Gibraltar to stay on three points.
It did not take long for Germany, with several World Cup winners back in the squad including captain Bastian Schweinsteiger, to threaten with Reus' powerful drive palmed on to the crossbar by keeper Giorgi Loria after five minutes.
With coach Loew reverting to a four-man defence from a three-player experiment against Australia in a friendly on Wednesday, the Germans were in and around their opponents' box for most of the first half.
Mueller fired at goal from a corner only to see the ball fly just wide and Mesut Ozil missed another big chance as the visitors had the hosts firmly on the backfoot.
Reus did better in the 39th when Mario Goetze charged into the box and was lucky to scramble the ball to the winger, who drilled home for his second goal this week, after also scoring in their 2-2 draw against Australia.
Mueller then fired in another on the stroke of halftime to firmly put them in the driving seat.
New Georgia coach Kakhaber Tskhadadze added a forward after the break but it was Reus who came close again, rattling the bar for a second time on the hour with another powerful shot.
"We are not yet fully on track and still have to improve," said Germany goalkeeper Manuel Neuer. "But there is sufficient time and I am very confident."
(Reporting by Karolos Grohmann, editing by Mark Meadows)
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