Highlights were scarce in the first period, but the hosts should have taken the lead in the 24th minute when Pedro Rios found himself clean through on goal, only to fire into the side netting.
Five players were shown yellow cards in the run up to the interval, and clear-cut chances were few and far between.
Sevilla were almost gifted the lead early in the second period when a botched clearance fell kindly for Kevin Gameiro, who sliced a half-volley wide of the mark.
The second period proved almost uneventful as the first, but Levante came close to snatching a winner six minutes from the final whistle.
It proved to be the last clear-cut chance of a forgettable evening of football.