The visitors managed to frustrate Juan Ignacio Martinez's side throughout the first half, but their good work was undone within 30 seconds of the second as Kone headed home his 15th league goal of the season.
Having conceded, though, Granada opened up and they were level midway through the second half as Odion Ighalo forced home the rebound after Gustavo Munua parried Franco Jara's shot.
However, Torres restored Levante's lead five minutes later with a thumping finish at the end of a fine team move and Valdo headed home from close range with six minutes remaining to secure all three points.
Kone is now within one goal of activating a clause in his loan-agreement with Sevilla that would see him have to return to his parent club next season, although he has announced his desire to remain with Levante, and he posed a threat.
The Ivorian was denied by a brilliant save from Julio Cesar with the only serious effort on goal in the first half, but was quickly rewarded in the second as he expertly nodded home Valdo's cross from the right.
Abel Resino reacted to the goal by introducing Jara and Igahlo in the search for an equaliser and he was rewarded after 67 minutes as the Nigerian prodded home after Munua could only parry Jara's effort back into the six-yard box.
However, Martinez made a crucial substitution of his own as Ruben Suarez replaced Jose Barkero and the diminutive winger was key as Levante regained the lead.
Suarez's tempting ball to the back post was nodded down by Valdo and Torres arrived just on cue to slam a volley high past Cesar from the edge of the area.
And Suarez and Valdo were again involved for the third goal as a dangerous counter-attack appeared to have lost momentum until Suarez fed Pedro Botelho on the left and his cross was fired past Cesar by Valdo for his third goal in five games.