The Valencia club are marooned in mid-table and have been off the pace form-wise, but managed to put a fine second-half performance together to take the win.
David Navarro and Pedro Lopez got the goals which pushed them up to 40 points and gave them an outside chance of making the Europa League qualifying spots.
They will need a number of more wins like this to make that happen, though, and future opponents may not be as inactive as Granada largely were throughout this clash.
They did start well as Jose Recio passed up an early chance and then Youssef El Arabi was also off the mark hitting at Keylor Navas when he could have done better.
But after watching Granada fail to take their chances, Levante went onto the front foot and before the break Ruben Garcia forced Roberto into a flying save to signal their intent.
The warning proved to be a valid one in the 48th minute as Navarro cracked in a loose ball to put his side in front.
Ruben Garcia tried to make it two with a lob that just went over before the home side stirred again with El Arabi and Manuel Iturra both hitting over when they should have done better.
It mattered little to Levante, though, who duly finished things off when he took in a Papakouli Diop pass with two minutes left.