The Catalan giants now trail leaders Atletico Madrid by three points having played one game more, as the season edges towards its conclusion.
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Following a largely uneventful opening to the contest, Barcelona managed to make the breakthrough on 24 minutes with their first real opening.
The goal allowed the hosts to move up a gear, with Pedro driving into the Getafe area before attempting to find the bottom corner, though Julio Cesar managed to pull off a fine save to deny the winger.
Despite looking as though the hosts were going to add to their lead following the opener, Getafe hit back through Lafita to level the contest on 37 minutes.
The midfielder controlled a high ball inside the Barca box before striking home to make it 1-1.
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Alexis Sanchez came close to regaining his side's lead before the interval, but he failed to make the most of his opportunity inside the box and struck an effort wide of the post.
Barcelona upped the pressure in search of a second goal, and Sanchez came close to finding one when he hit the crossbar after being played in by Alves.
Gerardo Martino's side did manage to find a second, though, and it was from the boot of Sanchez who stroked home from close range after some good work by Pedro.
It looked as though Barcelona were going to hold out for the three points, until Lafita struck once more in the dying seconds with a header to ensure that Getafe left with a point.