After a tentative opening from both sides, Levante midfielder Jose Morales registered the first shot on goal, but his 16-yard effort cleared the crossbar.
As the first half drew to a close, the visitors continued to have the better of the action, but, after Rodriguez forced another save out of Marino, Levante were able to reach the break on level terms.
Aaron and Rodriguez had chances soon after the restart, but they were given their clearest opening of the match midway through the half as Levante defender Tono committed a foul inside the penalty area.
However, Aaron squandered his opportunity from 12 yards, firing straight down the middle to allow Marino to make the save to keep Levante in the match with 20 minutes remaining.
The home side went straight up the other end, with Jose Mari firing wide from 25 yards before Rodriguez wasted another chance for Elche by heading off target.
With time running out, Cristian Herrera forced a solid save out of Marino at the near post, but a point is enough to ensure that Elche end the season in 13th place.