The closest Levante came to scoring was on18 minutes when a Pedro Lopez strike from just outside the Getafe box came back off the crossbar.
There were few clear-cut chances in the match, but Getafe came within a whisker of claiming all three points when Miguel Torres hit the bar in the final minute.
Levante climb two places to 10th, one behind Getafe.
Levante had five excellent scoring opportunities.
Roger made the biggest impact of any Levante substitute after coming on for Míchel in the 71st minute: he took two shots.
The three attempts by Robert Acquafresca were the most of any Levante player.
Getafe got off three shots, all of which were on goal, during the match.
Abdel Barrada had three shots for Getafe, more than any of his team-mates.
Miguel Angel Moya pitched in with five stops.
Sergio Escudero went off due to injury in the 81st minute and was replaced by Rafa.