The Portugal international inspired his side to a comfortable victory with a clinical triple in the second period of this derby clash, after the first half had ended goalless
Cristiano Ronaldo continued his scintillating form with a well-taken hat-trick that takes his tally in the league this season to 21, after Sergio Ramos had opened the goalscoring for the home side.
Jose Mourinho appeared to have one eye on the Copa del Rey semi-final against Barcelona this coming Wednesday as he rested players for this game, and it was only after Sami Khedira was introduced at half-time that los Merengues clicked.
Ronaldo looked the most dangerous player on the pitch in the opening half an hour, and twice came close to scoring only to be thwarted by Getafe's goalkeeper Miguel Moya.
Madrid continued to dominate possession as the first half wore on but did look susceptible on the break, as Diego Castro and the former Castilla player Pablo Sarabia stretched los Blancos' experienced back-line on more than one occasion.
Mourinho decided to change things at the interval after Madrid failed to score in the first half, as Khedira came on for Raul Albiol which resulted in Essien dropping into right-back and Ramos moving inside to centre-back.
The switch in personnel seemed to do the trick for the home side, as they took the lead in the 53rd minute through Ramos. The Spain international bundled home a corner after Moya failed to claim the cross, with the Getafe goalkeeper undoing some brilliant work moments before when he made a fabulous double-stop from Khedira and Angel Di Maria.
Madrid, looking a completely different side following the break, and went 2-0 up thanks to a blistering counterattack that was clinically finished by Ronaldo. The former Manchester United man hammered a shot low under Moya and into the bottom-right corner of the net having sprinted 70 yards to support Ozil and receive the ball on the edge of the Getafe box.
Within three minutes of that goal Ronaldo added a third. The Portuguese attacker's 20th league goal of the season came in the form of a close-range header after Di Maria had dinked an inviting cross to the back post which pulled Moya out of position.
In the 72nd minute Ronaldo completed his hat-trick from the penalty spot to make it 4-0 to Madrid, after Luka Modric had been fouled in the area by Alberto Lopo.
Madrid are now unbeaten in 22 matches at home in the league, but still trail Barcelona this season by 12 points.