Pogba set up Herrera for the opening goal just after half an hour into the match before adding the second himself prior to half time.
The Blues failed to register a single shot on target between the 11th minute and full time as their cup defence came to a disappointing end.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI (4-3-3): Kepa; Azpilicueta, Luiz, Rudiger, Alonso; Kante, Jorginho, Kovacic; Pedro, Higuain, Hazard
Subs: Caballero, Christensen, Zappacosta, Barkley, Hudson-Odoi, Willian, Giroud
STARTING XI (4-3-1-2): Romero; Young, Lindelof, Smalling, Shaw; Herrera, Matic, Pogba; Mata; Lukaku, Rashford
Subs: De Gea, Bailly, Dalot, Fred, McTominay, Pereira, Sanchez
CHELSEA SUBS: Caballero, Christensen, Zappacosta, Barkley, Hudson-Odoi, Willian, Giroud
MANCHESTER UNITED SUBS: De Gea, Bailly, Dalot, Fred, McTominay, Pereira, Sanchez