The former England defender, who won 57 caps for his country, replaced Stuart Pearce at the helm this summer, signing a three-year contract with the Under-21s.
Southgate will be tasked with improving England's showing in the European Championships this summer, which saw the country finish bottom of their section without a single point.
England are the only team in Group 1 yet to play a qualification match for the 2015 European Championships, with Lithuania sitting top of the section with seven points.
Moldova currently sit in fourth position having won one of their two matches, while Finland, Wales and San Marino make up the rest of the section.
England: Butland; Dier, Keane, Stones, Shaw; Hughes, Powell, Lingard, Redmond; Zaha, Kane
Moldova: Railean; Prodan, Jardan, Bogdan, Modirca; Rata, Matei, Anton, Carp; Focsa, Milinceanu
Sports Mole says: 3-0