The striker opened the scoring with a fine first-time finish before teeing up Pablo Piatti for the hosts' third, with Parejo following up his own missed penalty in between
Paco Alcacer opened the scoring just after the dismissal of Sergi Darder with a fine finish before Dani Parejo doubled the home side's advantage moments before the interval by converting the rebound from a missed penalty attempt.
Pablo Piatti sealed the points just 11 minutes into the second half when he rounded off a sweeping counterattack, as Valencia temporarily went top of the table.
Los Che had opened their Primera Division campaign with a 1-1 draw at Sevilla that came courtesy of a last-gasp goal from Lucas Orban - and in spite of the second-half dismissal of Rodrigo.
However, it was Malaga, who had beaten Athletic Bilbao 1-0 on match day one, who were reduced to 10 men at Mestalla, with Darder perhaps harshly seeing red just 27 minutes in for an allegedly reckless challenge on Parejo.
Valencia broke the deadlock just moments later when Paco got away from his man before guiding the ball home at the near post with a wonderfully instinctive finish from Jose Gaya's bouncing cross from the left wing.
Los Che made it 2-0 right on the stroke of half-time, Parejo converting at the second attempt after Carlos Kameni had saved the No.10's low spot-kick, which had been awarded for a handball by Weligton.
Valencia then put the outcome of the game beyond all doubt in the 56th minute, with Alcacer deftly laying the ball into the path of the onrushing Piatti, who found the bottom left corner with a sublime first-time strike.