The Leicester Tigers duo were included in the starting line-up, with Genge gaining a 20th Test cap and Youngs moving on to 101 after reaching his century in the Six Nations win over Italy a fortnight ago.
Club colleague Shalva Mamukashvili was named in the middle of the Georgia front row.
The first half was played at close quarters in the Georgia half of the field as tries from Jamie George (2), Jack Willis and Elliot Daly, followed by three conversions from Owen Farrell, gave England a 26-0 lead.
Genge and Mamukashvili were both replaced in the early stages of a second half which started in a downpour, and it took England almost 20 minutes to add to the score as George completed his hat-trick from another strong maul.
Youngs made way just after the hour mark, with the only remaining score coming from Dan Robson.
England face Ireland in the second Quilter International next Saturday.