The rare domestic reverse for Jose Mourinho's side, who were held to a 1-1 draw at home to Valencia last weekend, ended a 24-match unbeaten run in the league, their longest in 15 years.
They looked comfortably in control when Gonzalo Higuain fired them ahead from close range in the 27th minute at the Coliseum in Madrid.
But their failure to capitalise on long periods of possession ultimately cost them and lowly Getafe levelled eight minutes after the break when Juan Valera nodded past Iker Casillas from a free-kick.
It went from bad to worse for the visitors 15 minutes from time when substitute Adrian Colunga set up Abdelaziz Barrada to smash the ball high into the net and secure a famous victory.
Real's misery was compounded when defender Fabio Coentrao was sent from the bench for protesting late on and will be suspended for next weekend's match at home to Granada.
"We were unable to close out the game," Real's Spain midfielder Xabi Alonso said in an interview with Spanish TV.
"Obviously we have to improve and we are self-critical but we have to take things slowly.
"It was a setback we really weren't expecting and we have to change the dynamic as soon as possible."
Lionel Messi had earlier saved an off-colour Barca from a first defeat of the campaign when he struck twice in the second half in a 2-1 comeback victory at 10-man Osasuna.
Barca have six points from two games and top the table on goal difference from Rayo Vallecano, who also have six after their 2-1 win at Real Betis on Saturday.
Valencia failed to build on their impressive result at Real when they let slip a 2-0 lead and had Ricardo Costa sent off in a 3-3 draw at home to promoted Deportivo La Coruna in the late kick-off and are 12th on two points.
Real, who lost a league match for the first time after leading at the break in more than five years, have a solitary point and are down in 15th.
They now need to regroup for Wednesday's Spanish Super Cup second leg at home to Barca, when they will be attempting to overturn a 3-2 deficit from last week's first leg at the Nou Camp.
SHOCK LEAD
Barca fell 3-2 to Osasuna on a freezing February night last season but there was to be no repeat on a balmy summer evening in Pamplona as World Player of the Year Messi took his tally to four goals from two games.
Joseba Llorente gave the Navarrans a surprise 17th-minute lead when he hooked in at the far post from a tight angle.
Clad in their unfamiliar bright orange and yellow kit, Barca struggled to create chances and almost fell two behind midway through the second half when substitute Nino broke clear, but his shot spun out of play off the outside of a post.
The game turned in the 76th minute when Messi stretched to poke in an Alexis Sanchez centre, after which Osasuna midfielder Patxi Punal was shown a straight red card for his furious protests.
