The visitors twice came from behind before taking the lead for the only time late in the game, and owe a lot to goalkeeper Keylor Navas, who produced one of the outstanding goalkeeping performances of this season to keep his side in it.
Coke opened the scoring midway through the first half for Unai Emery's side but David Barral levelled a few minutes later from the penalty spot.
The Andalusians launched attack after attack on the Levante goal in the second half but were continuously denied by the saves of Navas, until Ivan Rakitic restored the lead on 68 minutes. But Loukas Vyntra pulled the visitors level, before Simao grabbed the winner with 15 minutes remaining.
But there was still time for more drama in injury time, with Nikos Karabelas seeing red for a late tackle on Jairo, who was then sent off a minute later for a shove on Barral.
Sevilla made the stronger start to the game, with Rakitic and Vitolo having the first efforts of the game.
They took a deserved lead after 25 minutes, Coke lobbing Navas from outside the area after cutting inside from the right wing. But just a few minutes later, Levante were awarded a penalty, Barral brought down by Federico Fazio just as he entered the area.
The striker picked himself up to take the penalty and took an unorthodox run up before stroking the ball into the centre of the net, sending Beto the wrong way.
Just a couple of minutes into the second half, Kevin Gameiro hit the woodwork after Navas had palmed the ball away from Vitolo.
Navas then made three saves in the space of a minute as Sevilla asphyxiated their opponents with pressure.
It looked as though it had paid off when they were given a penalty, Simao blocking a through ball with his hand. The Sevilla players called for the midfielder, already booked in the first half, to be sent off, but were left with just a penalty, from which Rakitic hit the post.
Navas then made two spectacular saves, diving low to keep out headers from Rakitic and then Coke. But a minute later Rakitic finally got the better of Navas, his shot taking a deflection on its way past Navas, the Croatian having picked the ball up from a short corner before trying his luck from just inside the area.
However, Levante were level again just three minutes after going behind, Vyntra heading in a corner swung in by Andreas Ivanschitz.
And it was not long before Joaquin Caparros' men were in front for the first time of the match, Simao bundling home the ball after Beto could only parry a close-range header from Barral following another Ivanschitz corner.
Sevilla continued to pepper the Levante goal but were unable to find an equaliser, and tensions shot up a notch as normal time elapsed, with Nikos and then Jairo being shown red cards in the space of a minute.
Sevilla then had one final go, Rakitic hitting a shot a couple of feet wide of the far post with injury time already up, Levante taking all three points despite managing just seven shots on goal compared to the 28 attempts from their defeated opponents.