Greenwood was perfectly placed in the opponents' box to take on a pass from Carles Alena and fire in his team's second goal just 15 minutes into the tie.
In the second half, the forward was found in plenty of space in a dangerous position, setting himself up and burying a shot low beyond the goalkeeper to extend his team's lead to six goals. He was substituted off minutes later.
Getafe ran rampant in the Copa del Rey match, running in a further six goals to make it 12-0 against their lower-league opposition.
Greenwood's goals are his second and third for the Spanish side since joining from Manchester United on loan.
The 22-year-old was loaned to the Madrid club after charges of attempted rape, controlling and coercive behaviour and assault occasioning actual bodily harm against him were dropped in February.
After an internal investigation as well as backlash from fans and members of staff, United opted against keeping him in the team for the current season.
Greenwood's bright start to life in Spain has sparked reports of a possible permanent move to La Liga, with Sevilla said to be interested in signing him.