Euro 2016 Qualifying: Georgia 0 Germany 2
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.
And it was another Bayern star in Muller who subsequently doubled the advantage with a drilled strike from just inside the penalty area, allowing the visitors to take their foot off the pedal.
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.
Georgia suffered a setback in the fourth minute when centre-back Alexander Amisulashvili was forced with an injury.
And the home defence soon came under considerable pressure, Reus smashing an effort against the crossbar after being played in by Muller in the sixth minute.
Muller then turned an effort narrowly wide of the left-hand post following a well-worked corner from Toni Kroos.
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.
Reus shot wide at the end of another free-flowing move on the half-hour mark. However, nine minutes later he atoned for that miss.
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.
Loria performed heroics to deny Reus and then Kroos before Gotze had a goal disallowed for offside.
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.