Cristiano Ronaldo and substitute Gonzalo Higuain were also on target, the former improving his record to 15 goals in his last six league games and eight in four against Getafe with a controversial penalty on the hour mark.
Miku netted a cool double for Getafe but it was not enough to prevent his side slipping to defeat.
Jose Mourinho's side headed into the encounter knowing Barcelona had dropped two points in a 2-2 draw at Real Sociedad earlier in the evening, and looked keen from the outset to steal an early march on the champions.
Angel Di Maria burst into the area in the fourth minute only to be denied by the feet of Miguel Moya from the right side of the six-yard box, and then he cut inside and unleashed a left-footed shot into the side-netting.
The lively Argentinian turned provider in the 10th minute with a cross for Ronaldo, whose powerful header from 12 yards was tipped over by Moya.
There was a chink of light for Getafe at the other end two minutes later when Miku got clear, but he took too long over his shot and Sergio Ramos got back to block.
However, in the 14th minute, Madrid went ahead with a well-worked goal.
Mesut Ozil was influential in a neat move also involving Marcelo and Fabio Coentrao, the German eventually teeing it up for Benzema to take a touch and place into the top-right corner.
Coentrao should have doubled the hosts' lead in the 34th minute when he was played in by Marcelo down the left-hand side of the area, but he dinked his shot just wide.
For all their dominance, Madrid remained only one goal clear and that lead was almost wiped out eight minutes before the interval when Marcelo, in an attempt to cut out a right-wing cross, sent a looping header over Iker Casillas but was saved by the woodwork.
That should have served as a warning to Mourinho's side as to how slender their advantage was, but two minutes later they were pegged back. Mehdi Lacen fed a slick ball through to Miku - who was onside despite the Madrid protests - and he slotted past a helpless Casillas and into the bottom-left corner.
Coentrao passed up a gilt-edged chance to restore Madrid's lead early in the second half, his follow-up finding only the side-netting after Ronaldo's shinned overhead-kick from Benzema's cross had come back off the inside of the post.
The hosts had the ball in the visitors' net in the 54th minute but Coentrao - again at the centre of things - was adjudged offside when Benzema's ball deflected in off him.
Getafe were still very much in the game, though, and required Casillas to beat away another blast from Miku in the 56th minute.
The tide turned in Madrid's favour for good, however, when referee Carlos Clos Gomez awarded the hosts a penalty for a supposed foul by Cata Diaz on Ronaldo, although any contact looked to be outside the box.
The former Manchester United man picked himself up to send the spot-kick into the bottom-right corner.
Ronaldo then helped his side extend their lead with a sublime cross-field pass for Benzema, who was left with a straightforward finish to make it 3-1.
Getafe refused to lie down, though, and it was game on again in the 73rd minute when substitute Dani Guiza saw his shot parried by Casillas and Miku kept his composure to steer home the rebound with his left foot.
Higuain had had to wait patiently on the bench for 86 minutes but, when he eventually came on in place of Ozil, he needed only two minutes to make his mark.
The Argentinian got the better of Juan Valera and Miguel Torres on the edge of the box before firing a low shot past Moya to seal the win.