Sergio Ramos celebrated his return from injury with the match-winner on 18 minutes, muscling in to head home a Mesut Ozil corner from six yards.
While Madrid failed to add to the veteran defender's goal they were rarely threatened and were able to afford the second-half profligacy of Karim Benzema.
The win strengthened Jose Mourinho's side position ahead of Barcelona at the summit.
Getafe, unbeaten in six league games before Saturday, offered little as an attacking force, although they could have led early when Diego Castro side-footed what was to be their best chance over after three minutes.
Madrid then took over and should have had a penalty after 15 minutes when Cristiano Ronaldo appeared to be barged over by Miku as he tried to run on to a through-ball.
Madrid's protests soon gave away to celebration, however, as Ramos netted the decisive goal.
Ozil fizzed in a dangerous cross to the top of the six-yard box, although Ramos still needed to be strong to get on the end of it and send his header into the far corner.
Madrid failed to replicate Ramos' single-mindedness for the remainder of the match, however, as they failed to kill off a laboured Getafe side.
Kaka wildly shot over with his left foot from 10 yards, while Ronaldo scuffed a first-time shot wide after the home defence helped Alvaro Arbeloa's cross into his path.
Madrid continued to dominate without finding a second goal after half-time with Benzema failing to convert a couple of clear-cut chances.
The best of those arrived on 62 minutes when he raced in behind the defence but home goalkeeper Miguel Angel Moya was out quickly to block.
Moya had looked less assured when he flapped a swerving Ronaldo shot away, while Benzema blazed over soon after when he was freed at the back post.
Benzema made way for Gonzalo Higuain after 73 minutes and the substitute was only denied a goal when his curling goal-bound effort was kept out by a diving Moya.
It did not matter, though, as Madrid had done enough to ensure rivals Barcelona kicked off their late game 10 points behind.