Levante and Europa League champions Atletico Madrid started their respective La Liga campaigns with a point each at Ciudad de Valencia.
Nabil El Zhar scored his first goal since joining Les Granotes last summer to put the hosts ahead on five minutes.
Arda Turan levelled the scores 17 minutes later with a fizzing strike from outside the box.
Falcao went close to winning the match for the visitors late on, but his athletic header landed narrowly wide.