The French centre-back struck just before half-time to give the visitors the lead in what was a largely uneventful match at the Coliseum Alfonso Perez.
Getafe, meanwhile, missed an opportunity to gain ground in their bid to qualify for the Europa League, and remain in ninth place in the table.
The first chance of the game fell to Roberto Soldado, who headed well over the bar after a cross from the left hand side from Andres Guardado. Getafe's first attempt, coming after 14 minutes, was also a header, which Fede Fernandez could not direct on target from a corner.
Getafe forward Adrian Colunga had to be substituted after just 18 minutes after picking up an injury, and was replaced by Angel Lafita, who picked up a booking just 10 seconds after coming on, for a dangerous challenge on Guardado.
Pedro Leon and then Soldado both sent long-range efforts high into the stands and just as the first half seemed destined to finish goalless, Mathieu broke the deadlock. Valencia attacked in numbers and the Frenchman received the ball from Ever Banega just outside the area to slot into the far bottom corner with the inside of his boot.
After a fairly even first half, Valencia went onto control the second, but could not add to their goal.
Miguel Angel Moya did well to deny Soldado just after the break, the striker controlling a long pass by Guardado, but was unable to shoot past the Getafe stopper. Moya then had to be alert to make a double save from Jonas, and late on prevented Mathieu from doubling his tally for the afternoon, pushing away his shot from the edge of the area.
Valencia could have wrapped up the game in the final minute when Sofiane Feghouli raced towards goal with Guardado to his left, but the Algerian decided to go it alone and his shot went high over the bar. Two minutes later, it did not matter, as the final whistle blew to signal Ernesto Valverde's side's third straight victory.