Lisandro Lopez and Alvaro Arroyo scored in a six-minute spell either side of half time as the home side moved a point clear of their visitors in the table.
Celta have now gone four games without a win and remain with just a single victory this term.
David Rodriguez had the first effort on goal for Celta but Miguel Moya in the home goal was equal to it.
The visitors suffered a blow in the 18th minute as Carlos Bellvis was forced off with an injury and replaced by Jonny Castro.
But they still looked the more threatening as Dane Michael Krohn-Dehli brought another save out of Moya with a 25-yard free kick.
Pablo Sarabia had Getafe's first meaningful attack as the half-hour approached and he should have done better as he fired wide from eight yards.
The visitors were still applying the more pressure as Barcelona loanee Rafa Alcantara shot wide before Roberto Lago blazed over the bar down the other end.
Celta may have had the better of the first half but it was the home side who took the lead as Pedro Leon's corner was met by Lopez who headed home from six yards in the 44th minute.
Alexis Ruano put a close-range header wide early in the second half and Celta were made to pay as Getafe doubled their lead in the 51st minute.
Lopez provided a flick across goal and Arroyo met it with a header of his own to beat Moya.
Celta provided some pressure as they fought to get back in it but Getafe held out for a comfortable win.