Marcelino's side ensured that they will end the weekend in third place with a second consecutive win courtesy of late strikes from Francis Coquelin and Daniel Parejo, the latter of which came from the penalty spot after the hosts had been reduced to 10 men.
Brown Ideye had earlier given Malaga the lead, but the defeat leaves the home side still seven points from safety as their wait for a league victory stretches to nine matches.
Malaga went into the match having scored just one goal during an eight-match winless streak in La Liga and having failed to find the back of the net in front of their own fans since November 19, but that barren spell was finally ended shortly before the half-hour mark.
Ideye was the man to supply the long-awaited strike, finding space inside the area to convert Recio's delivery and give the bottom club a surprise lead over their Champions League-chasing visitors.
Valencia struggled to conjure a response and thought they had fallen two goals down 11 minutes into the second half, only for Youssef En Nesyri's effort to be disallowed for a foul in the buildup.
Indeed, it took until 10 minutes from time for the visitors to even register a meaningful shot on goal, but they took full advantage of that as Coquelin nodded Parejo's cross home for his first Valencia goal since his January move from Arsenal.
That sparked a late collapse from the hosts, and their hopes of holding out for a valuable point in their battle against the drop was made even more difficult when Ignasi Miquel was shown a contentious red card for a foul in the area which also gifted Valencia a penalty six minutes from time.
Parejo stepped up for the visitors and duly added insult to injury by firing home from the penalty spot, completing the late turnaround to keep Valencia at arm's length of fourth-placed Real Madrid.
MALAGA (4-4-2): Jimenez; Rosales, Hernandez, Miquel, Gonzalez; Lestienne (Keko, 68'), Recio (Lacen, 73'), Iturra, Castro (Rolan, 83'); Ideye, En Nesyri
VALENCIA (4-4-2): Neto; Vezo, Gabriel, Murillo, Gaya; Soler (Torres, 80'), Parejo, Coquelin, Guedes; Vietto (Rodrigo, 60'), Mina (Zaza, 61')