Malaga were looking to avenge last season's 3-0 reverse at the Estadi Ciutat de Valencia but the plan went off the rails when Jose Barkero put the home side in front with a 27th-minute penalty.
Isco restored parity through a spot-kick in the 37th minute and then sealed the points with a neat finish just after the restart.
Malaga's Vitorino Antunes had the first shot of the match but his modest 12-yard attempt did not require a save.
Levante went much closer on the quarter-hour mark, Michel crossing for Ruben Garcia, whose close-range header was superbly beaten away by Willy Caballero.
Malaga again relied on Caballero to keep them level when he improvised to save with his feet from Obafemi Martins.
The hosts were producing the more coherent attacks and opened the scoring in the 27th minute from the penalty spot.
Martins won the decision when he was fouled by Martin Demichelis and Barkero stepped up to despatch the spot-kick.
It took Malaga 10 minutes to equalise via a spot-kick of their own, Christian Lell taking down Julio Baptista and Isco slotting home from 12 yards.
The leveller came against the run of play but Malaga might have led at half-time had Gustavo Munua not tipped Baptista's 25-yard effort round the post and then punched Joaquin's follow-up clear.
The visitors did go in front two minutes into the second period, Jeremy Toulalan crossing from the right wing and Isco converting right-footed from the centre of the box.
It took Levante 20 minutes to respond, Lell and Martins both denied by Caballero and Barkero floating a free-kick over the bar as they finally exerted some pressure.
The hosts could not find the goal they needed though, substitute Juanlu heading their last meaningful attempt wide.