Goals from Jonathan Viera and Joaquin Larrivey stopped the rot for the visitors and they now join their opponents on 12 points just above the bottom three.
Despite the need for points from both sides, it took 24 minutes and a goal from Viera to finally bring the match to life.
Defender Tito sparked events with his move down the right wing before sending a pass into the area, where Viera was waiting to stab home into the bottom right corner.
Alejandro Galvez tried to double the advantage eight minutes later but curled a 30-yard free-kick over the bar.
Viera was also wasteful with his right foot as Vallecano threatened to take a stranglehold on proceedings, while team-mate Alhassane Bangoura had a better chance to make it 2-0 four minutes before the interval but spooned his shot over the net.
Celta Vigo had won two of their last three matches, scoring six goals in the process, but appeared to have forgotten how to shoot until just before half-time when David Costas put a header past the post.
However, Vallecano quickly regained their edge in the second half and home goalkeeper Yoel had to be alert to tip Roberto Trashorras' dipping free-kick over the bar.
Rafinha tried to pull Celta level with a shot from the edge of the area which was comfortably dealt with by Ruben in the Vallecano goal.
But it was no suprise when the visitors broke through for a second after 72 minutes. Larrivey met a cross into the area from Adri Embarba before planting a header home from a few yards out.
There was no way back for Celta now and the best they could muster in response were weak attempts from Michael Krohn-Delhi and Hugo Mallo.