The game finished goalless, leaving their hopes of progressing to the knock-out stages of the competition hanging in the balance.
Barcelona’s 18-year-old winger Yusuf Demir, signed on loan from Austrian side Rapid Wien in July, hit the crossbar before defender Ronald Araujo had a goal disallowed.
Benfica’s est chance came in the dying seconds of the game, when striker Haris Seferovic missed a shocking open goal.
The result leaves Barcelona are two points clear of Benfica heading into their final group game against Bayern Munich at the Allianz Arena in December.
Benfica, meanwhile, host Dynamo Kyiv. The Ukrainian outfit have picked up just a point in this season’s Champions League so far.
Barcelona will drop into the Europa League if Benfica beat Kyiv and they fail to beat Bayern, who have won all five of their European games this term.
And Xavi – who succeeded Ronald Koeman as the Catalan club’s new manager earlier this month – is fearing the worst, despite praising his team’s performance.
“We were far superior to Benfica and we played a great game, we only missed the goal,” said the Spaniard. “If we had scored, we would be talking about a great game.
“I’m still optimistic. We’re Barca, we have talent and players to make a difference. But today we added one point and that’s not Barca worthy.
“Today we have seen that there is no physical issue. What we must do is regain the confidence of the players who can score goals. We will see what we can do on the market in January.”
Barcelona have endured a chaotic calendar year, reportedly racking up more than £1billion worth of debt and losing captain Lionel Messi to Paris Saint-Germain.
The team suffered a dreadful start to the season under previous manager Koeman, with Xavi trying to salvage a top-four finish in La Liga.
Barcelona are currently seventh in the table, ten points behind leaders Real Madrid and six behind champions Atletico Madrid in fourth.
“They support us through thick and thin. I have never seen the Camp Nou in this way, it’s priceless and you have to take advantage of it.
“We depend on ourselves, we go to Munich with the intention of winning. It will be difficult, but we’re in good spirits.”
If Barcelona drop into this season’s Europa League, they could face Leicester, West Ham or Rangers in the knock-out stages.
Manchester United and Chelsea, meanwhile, have both progressed to the last 16 of the Champions League after recording wins on Tuesday.
The Red Devils defeated Villarreal 2-0 in Spain, while the defending champions hammered Juventus 4-0 at Stamford Bridge.