The away side had a chance after just four minutes when Borja Fernandez met a free kick with a header, but the goalkeeper kept it out before the rebound was put wide.
Despite Getafe's strong start, it was Osasuna who took the lead on six minutes through Oriol Riera, who beat the offside trap and expertly lifted it over the keeper to make it 1-0.
The game was end to end, with both sides counter attacking at pace when they win the ball in their own half.
Lafita came close on 36 minutes when he met Pedro Leon's deep cross with a header, but his effort clipped the outside of the post and bounced wide.
Adrian Colunga almost grabbed an equaliser on 57 minutes after driving into the box and firing under Fernandez, but the ball was cleared off the line.
Colunga had a wonderful chance to bring his side level when he latched onto a ball in the area, but Fernandez rushed out and saved well.
Getafe pushed for a late equaliser and caused a scramble in the box late on, with Colunga and Leon having strike on goal, but Osasuna stood firm and cleared.
The hosts wrapped up the game on 88 minutes when Roberto Torres broke clear and slotted past the goalkeeper to make it 2-0.