The east-coast outfit reached 36 points and 10th place courtesy of the stalemate - their highest-ever points tally at this stage of a La Liga season - but they were left to rue a chronic lack of incision in front of goal.
Visiting goalkeeper Miguel Moya deserved praise for keeping Robert Acquafresca and Pedro Rios at bay in the first half but in truth, ninth-placed Getafe were lucky to escape with a point.
Both sides are battling for a possible place in Europe for next season but the early exchanges suggested Levante wanted it more.
On-loan Bologna striker Acquafresca tested Moya's reflexes with a searing strike from distance and the Getafe keeper did well to repel the ball with his feet.
Getafe rallied briefly, Jaime Gavilan warming Gustavo Munua's palms from outside of the box, but Acquafresca soon forced his way back into the game.
The Italian drew a nervous parry from Moya before Ivan Lopez rattled the crossbar with a curling shot from 20 yards.
Rios should have done better with Michel's inswinging cross, instead nodding the ball into Moya's arms, but the former did make Getafe's keeper deflect his rocket in the 36th minute.
Levante might have dominated the first half but they had Abdelaziz Barrada's malfunctioning radar to thank before the break as the Getafe midfielder scooped a dangerous ball just over the bar.
There was little more to cheer following the restart as a largely attritional period saw Rios injured and replaced by former Liverpool winger Nabil El Zhar.
The Moroccan's introduction reignited Levante's bid for all three points, though, and Acquafresca came very close to converting a header from El Zhar's corner.
Another home substitute, Marti Roger, tried his luck from the edge of the box in the 86th minute but his left-footed effort did little to trouble Moya.
Time was running out for Levante to convert their overwhelming domination but they pressed on and nearly snatched a late winner through Vicente Iborra.
When Alexis conceded a free-kick on the edge of the Getafe box, Juanlu passed to Iborra instead of shooting, but the surprise move was only good enough to rattle the crossbar and the points were duly shared.