Marseille winger Rowe provided the crucial moment in the 92nd minute as England secured their fourth Under-21 Euro title, moving one ahead of Germany and just one behind joint record five-time winners Spain and Italy.
England raced into a fifth-minute lead as Liverpool midfielder Harvey Elliott collected a loose ball and calmly stroked in his fifth goal of the tournament.
Carsley's side threatened to run riot as they regularly cut Germany open on the counter-attack, and Omari Hutchinson drilled in their second goal 20 minutes later.
Nelson Weiper dragged his team back into the contest in first-half stoppage time, powering Paul Nebel's cross into the net with a bullet header.
The Germans drew level just after the hour by Nebel and almost grabbed victory in injury time, but England reclaimed the lead in the second minute of extra time, as Tyler Morton's brilliant cross was headed home by substitute Rowe.