The visitors had made a promising start to the game and caused problems for Valencia early on but the game changed completely when Malaga midfielder Sergi Darder was sent off.
Paco Alcacer opened the scoring moments later to ensure Valencia took full advantage and then Dani Parejo extended the gap just before half-time.
Pablo Piatti then struck an impressive third goal 10 minutes into the second half to cap an ideal home debut for Espirito Santo.
Malaga forward Roque Santa Cruz nearly gave Javi Gacia's men an early lead, firing just wide of a post from outside the area.
Sofiane Feghouli had the hosts first chance of the game, arriving in the box to head a cross from left-back Jose Gaya at goal, but the Algerian's effort fell just a couple of feet wide of the far post.
Midway through the first half Malaga had two chances to go in front in the space of a minute. First Luis Alberto found space and tried his luck from range, his low shot fisted away by Diego Alves. From the resulting corner Santa Cruz got on the end of a cross at the near post, but headed a few feet wide from point-blank range.
However, the visitors' hard work was undone by a moment of carelessness from Darder, who was given a straight red card for a high-footed challenge on Parejo in the 27th minute.
Valencia took advantage almost immediately, the lively Gaya finding Alcacer in the area, and the young striker fired low into the bottom corner to mark his call up to the Spain squad in style.
Ricardo Horta could have equalised with an effort from outside the box but Alves was able to tip it over the bar, and then the visitors' hopes of getting back into the game were dealt a lethal blow just moments before the break.
Valencia burst forward and Feghouli tried to release a team-mate with a low pass into the box, but Malaga defender Weligton went to the ground and blocked the pass with his hand, giving the referee little option but to award a penalty. Parejo's spot-kick was saved by Malaga goalkeeper Carlos Kameni, but the midfielder followed up his shot and sent the ball back into the net.
Malaga should have pulled a goal back early in the second half but Juanmi's close range effort was chalked off incorrectly for offside.
Then Piatti piled more misery on the visitors, scoring the pick of the games' goals.
Feghouli picked out Alcacer on the edge of the area, and the striker teed up Piatti, who smashed the ball into the far corner with a stylish half-volley, putting an extra shine on the night for Los Che.