The stalemate means leaders Atletico Madrid can stretch their advantage over second-placed Barca to six points with two games left, including a visit to the Nou Camp on the final day of the season, with a win at Levante on Sunday.
Real Madrid are three points adrift of Barcelona in third with two games in hand, including Sunday's match at home to Valencia and Wednesday's trip to struggling Real Valladolid.
The Barca players and fans paid a moving tribute before kickoff to the club's former coach Tito Vilanova, who died last month following a battle with throat cancer.
The match appeared to be going according to plan when Lionel Messi, who played under Vilanova as a teenager in the Catalan club's academy, made it 1-0 in the 23rd minute when he stroked a Dani Alves centre high into the net.
It was the Argentina forward's 28th goal of an injury-disrupted campaign, two fewer than La Liga top scorer Cristiano Ronaldo of Real and one more than Atletico forward Diego Costa.
Getafe snatched the first of two surprise equalisers eight minutes before the break when Angel Lafita controlled the ball on his chest in the area and fired low past goalkeeper Jose Manuel Pinto.
Barcelona continued to dominate early in the second period without creating many clear chances, although Messi forced a fine save from Julio Cesar and the ball ricocheted off Alexis Sanchez on to the bar.
The introduction of Barca's Spain playmaker Cesc Fabregas just after the hour gave them some extra zip and it was his cross that eventually found its way to Alexis in the 67th and the Chile forward fired a first-time effort into the corner.
Barca were again guilty of failing to turn dominance into the goals that would have killed off the game and Jaime Gavilan found space on the left in the 92nd minute and crossed for Lafita to head superbly past Pinto.
Getafe, who have won two of 21 matches since the end of November, remain in serious peril three points above the relegation places.
Athletic Bilbao, who are fourth on 68 points, claimed a spot in next season's Champions League playoff round with a 3-0 win at ninth-placed Rayo Vallecano on Friday.