It was his side's first match of the qualifying process for the 2015 European Championships, which will be hosted by the Czech Republic.
New boss Southgate handed a first start at Under-21 level to West Bromwich Albion attacker Saido Berahino and he rewarded the faith shown in him by scoring the only goal of the game against Moldova.
Mika Laurikainen's side currently top Group 1, having collected seven points from their first three matches. Last time out they defeated their Lithuanian counterparts 1-0, before which they recorded a 5-1 win over Wales, with Vayrynen scoring a hat-trick.
Finland U21s: LLWDWW
England U21s: WWLLLW
Possible starting lineups
Finland U21s: Joronen; P O'Shaughnessy, Hatakka, Aspegren, D O'Shaughnessy; Paananen, Lod, Yaghoubi; Vayrynen, Alho, Kastrati
England U21s: Butland; Wisdom, Keane, Stones, Shaw; Chalobah, Redmond, Ward-Prowse, Berahino, Carroll; Zaha
Sports Mole says: 1-2