The Valencia-based side had midfielder Papakouli Diop red carded for a high challenge after 53 minutes and, as the hosts weathered a late siege, defender Pedro Lopez got a second booking.
After being knocked out of the Europa League at the last 16 stage by Rubin Kazan in mid-March, Levante have suffered a dramatic loss of form.
They have won only one of their last eight La Liga games but Friday's draw leaves them in 12th place with 42 points and three matches left to play.
Zaragoza's bid to avoid the drop has stalled after two straight wins to leave them 16th with 34 points, two points above the relegation zone.
- Sports & Recreation
- Rubin Kazan