Jon Ander Olasagasti had an ambitious early effort for the hosts, but he sprayed wide from the centre circle when attempting to catch the Sevilla goalkeeper off his line.
The opener came at the other end, though, when Robbie Ure was gifted his first goal in Spanish football. A poor, underhit back pass by defender Ifeanyi Ndukwe handed possession to the striker, who simply had to round Mathew Ryan and slot home.
It took the Frogs a while to muster a response, but Adrian de la Fuente did force a fine stop out of Odysseas Vlachodimos with a low drive from distance that was heading into the bottom corner.
It was Luis Garcia Plaza’s men who would finish the half strongest though, as signalled by Youssouf Fofana poking straight at Ryan after making a darting run into the box for the visitors.
The Frenchman then sent a free-kick over the bar, before Juan Iglesias had a 30-yard drive beaten away and Ure scuffed wide from near the penalty spot as Levante managed to survive to the break with just a one-goal deficit.
The visitors maintained their momentum once the second half got underway, but Ure wasted another opening and Miguel Sierra saw his fizzing strike brush Ryan’s fingertips before clattering into the bar.
A second goal looked inevitable, and it duly came through Felix Correia, who tucked home from close range after profiting from Ure’s knockdown in the box.
That two-goal lead lasted merely seconds though, with Levante going down the other end and halving the deficit through Isaac Romero, who pivoted and lashed past Vlachodimos at his near post from a tight angle.
He could have had another when seeing a bobbling strike from outside the area saved, that coming after Ure should have put Sevilla out of sight at the other end when released one-on-one, only to drag wide.
It looked like things were petering out after that, but the signalling of eight minutes added time gave Levante hope, and they duly levelled when the ball fell to Dela on the edge of the area, and he swung a long limb at a dropping ball, guiding it perfectly into the back of the net.
There was more drama to come though, with Romero breaking forward just moments later and beautifully firing into the top corner from 25 yards.
His evening was soured after picking up a second yellow card for his celebration, and that proved costly as Levante somehow grabbed another equaliser when, after Dela and Nacho Perez had seen close-range strikes saved, Ndukwe atoned for his earlier error by bundling home.
The result means Levante move out of the relegation zone after avoiding a third successive defeat, whereas Sevilla miss out on the chance to move within two points of fourth-placed Real Madrid.
Flashscore Man of the Match: Robbie Ure (Sevilla)