El Hamdaoui volleyed in Vitorino Antunes' out-swinging cross to open at their La Rosaleda Stadium in the 31st, and nine minutes later the former Ajax played generously squared the ball for Francisco Portillo to make it 2-0.
Malaga's Eliseu Pereira put the result beyond doubt three minutes after halftime with an unstoppable shot inside the far post.
El Hamdaoui finished off a great team buildup in the 62nd with the ball passing through the legs of Portillo, Pedro Morales and Jesus Gamez before he pushed it home.
He then used a hard left-footed strike to drive his third goal between the goalkeeper and the post to cap Malaga's much-needed victory.
"What we saw today was what we were lacking, a great win, with five goals," said Schuster. "We took a step forward today."
Valencia's sloppy passing helped Jorge Molina put Betis ahead in the ninth, and the striker threaded a through ball for a charging Sevilla to fire by goalkeeper Diego Alves in the 22nd.
Diego Alves made the first of several saves to deny Molina in the 32nd, but he failed to stop Sevilla from poking the ball between his legs in the 35th for his second goal of the night.
Valencia defender Ricardo Costa pulled one back with a header from a free kick in the 67th, but his team never threatened after.
"We are trying to improve, but we gave too much away and it's difficult to win playing like that," said Valencia coach Miroslav Djukic. "We lose the ball too easily. We need to keep it simple and play more long balls if we can't make the short pass."
Valencia hosts Swansea on Thursday in the Europa League while Betis welcomes Lyon.
Espanyol's victory at Los Carmenes Stadium kept the Barcelona-based side unbeaten through four rounds to start the season.
Lanzarote gently curled the ball off the post and into the net from a free kick inside Granada's area awarded to Espanyol after the referee ruled that goalkeeper Roberto Fernandez had handled a back pass from a defender.
Televised replays showed that the ball appeared to take a deflection off an Espanyol player, suggesting that the free kick should not have been given.
Granada's tempers boiled over in the 82nd when substitute Odion Ighalo received back-to-back bookings, both for protesting to the referee.
"It felt like an evenly-matched game and that we had to stay alert to take our chances," said Espanyol coach Javier Aguirre. "It looked like a sure 0-0 that could only be broken with an individual action, and that's where Manu Lanzarote was great."
Miku's goal-scoring performance for Getafe helped ruin the debut of Osasuna's new manager Javi Gracia, who replaced the fired Jose Mendilibar two weeks ago.
Osasuna started brightly on the road in Madrid with Roberto Torres scoring in the 24th, but Miku headed in a corner kick that had sailed over goalkeeper Andres Fernandez to level in the 35th.
After his acrobatic kick had sent the ball off the woodwork, Miku used a nifty touch to slip the ball under a defender before placing his second goal just inside the post in the 52nd, sending Getafe on its way to its first win of the season.
Osasuna almost grabbed the draw when Oriol Riera hit the crossbar in the 85th, but it remained the only team yet to take a point in Spain's topflight.
