Koeman team where also beaten 3-0 by Bayern Munich earlier this month – have lost their opening two matches in the competition for the first time, and sit bottom of Group E.
Benfica got off to an energetic start and opened the scoring inside three minutes, when Darwin Nunez cut inside and finished low into the near corner.
Rafa Silva then clipped in a second after the break and Nunez netted a penalty in a comfortable victory for the home side.
Nunez also hit the post from out wide after rounding stranded Barcelona goalkeeper Marc-Andre ter Stegen, who made a rash decision to charge out of his area.
Luuk de Jong missed a glorious chance to level for the visitors early in the first half when presented with a seemingly open goal.
But koeman team only registered one effort on target and had Eric Garcia sent off for a second booking with three minutes remaining.
Defeat means Barcelona face the prospect of not making the knockout stage for the first time since the 2003-04 season, when they did not qualify for the Champions League as the pressure piles up on koeman.
The last time they failed to progress from the first group stage when playing in the competition was in the 2000-01 campaign.
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