The world champions recalled Muller, Bastian Schweinsteiger - making his first appearance since last year's World Cup final - Toni Kroos and Mats Hummels to their starting XI, having rested the quartet for a 2-2 friendly draw with Australia on Wednesday.
Germany travelled to Tbilisi knowing they could ill-afford to come away with anything other than victory and the gap in quality was evident throughout at the Boris Paitschadse Stadium as the visitors dominated from start to finish.
After spurning a host of early chances, Germany moved ahead through Reus in the 39th minute following excellent work from Bayern Munich's Mario Gotze.
Reus struck the woodwork - for the second time - during a largely uneventful second half, but that was as close as Joachim Low's men came to a third goal as they moved alongside Scotland and Poland on 10 points at the top of Group D ahead of the latter's clash with the Republic of Ireland.
Germany continued to display profligacy in front of goal despite dictating matters, Mesut Ozil failing to take advantage of Giorgi Loria's inability to deal with a Muller cross as he sent a tame volley straight into the goalkeeper's grasp.
The Borussia Dortmund forward curled home a low, close-range shot after former team-mate Gotze had twisted his way past four defenders with a jinking run into the box.
Yet Georgia's defence was breached for a second time a minute before the interval, Muller collecting Ozil's pass and firing into the bottom-right corner.
Reus shot against the bar from Sebastian Rudy's right-wing delivery on the hour mark to briefly light up a second half that had until that point only been noteworthy for a pitch invasion from one supporter, which was replicated in injury time.
Schweinsteiger and Jaba Kankava picked up yellow cards following an altercation, but Germany kept cool heads thereafter as they saw out the game with comfort to boost their hopes of topping a tightly contested group.
