The Reds' captain scored twice before half-time against the German side to seal a victory in former Totenham coach Alex Inglethorpe's first game in charge of the youth team
Coady, who made his senior debut for Liverpool in a Europa League clash against Anzhi Mackhakala earlier this month, scored twice in the space of four minutes to give his side the lead at the interval, before Morgan’s late strike wrapped up the points in Alex Inglethorpe’s first game in charge of the Reds’ second string.
Liverpool lost their first three games in the competition but remain undefeated domestically, dominated from start to finish, and head into their final game with Inter Milan with their destiny in their own hands.
Dortmund, who beat the Merseyside team 2-1 when the two sides met in Germany, barely threatened Ryan Fulton in the Reds' goal, with defeat ending their participation in the competition and dooming the German side to last place in Group 5.
After an even start Liverpool slowly started to take control, forcing Dortmund goalkeeper Cedric Wilmes into making a number of saves early on with strikes from distance.
The Reds took the lead mid-way through the first half when Krisztian Adorjan's clever through ball picked out full-back Brad Smith, who floated in perfectly weighted cross to the far post, which left Coady free to tap home with a simple header to open the scoring.
Liverpool doubled their lead minutes later from the penalty spot after Morgan was tripped when trying to round Wilmes, allowing Coady to step up to net his second goal of the evening.
Inglethorpe’s side could have been out of sight at the break with lively wingers Marc Pelsoi and Jorban Ibe both going close, before Morgan had a shot acrobatically cleared off the line after Adorjan had done well to pick the young forward out.
Dortmund fought back in the second half but never looked like troubling the score-line. Adorjan could have made it 3-0 when he saw his clever flick bounce back off the post after Ryan McLaughlin had picked him out.
Morgan finally did get his name on the scoresheet, after rounding Wilmes and rolling the ball into the empty net following a pinpoint through ball by Adorjan, and could have made it 4-0 minutes later only to see his curling effort from the edge of the area cannon off the underside of the bar.The Reds saw out the rest of the game in style with their job comofortably done, and now prepare for their decider against Inter, which will take place early in the new year.