The defeat, Barcelona's first in 19 league matches, gave La Liga title race back to Real Madrid.
Barcelona, coming off the greatest comeback in Champions League history with a 6-1 defeat of PSG on Wednesday, went down just before half-time on Sunday thanks to a Joselu strike.
Barca entered in first with 60 points, one more than Real Madrid, with this match serving as a chance to remain atop La Liga table.
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Luis Suarez drew Barcelona level quickly after the break, but Alex Bergantinos, making a rare start for Deportivo, netted the victor with 16 minutes remaining.
The goalkeeper earlier in the game should have been sent off for a clear foul when he was the last man, reports Xinhua news agency.
With Deportivo coming into the game unbeaten in three matches since Pepe Mel took charge at the start of the month, this was always going to be a hard fixture.
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LUIS SUAREZ'S incredible run of winning when he finds the back of the net ground to a resounding halt on Sunday... after 72 games. They grew in confidence and we made errors. We didn't have the necessary fluency to overcome their style but we were growing and ended up making mistakes.
"The PSG result did not cost us today, we've had enough days to recover. The pressure is there, it doesn't end here, there's still a lot to play for and we know that", Real coach Zinedine Zidane told his club's website.
The Blaugrana's 6-1 win over Paris Saint-Germain not only qualified them for the quarter finals, with the side duly instilled as favourites for the tournament once more, but it has also renewed a sense of belief among fans and players alike.
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In fact, in the 72 games Suarez has scored in for Barca, the Catalan giants won 67 times, drawing five. losing none.