Mauricio Pochettino's side have given themselves hope of qualifying, but take on one of the tournament favourites who have already secured top spot in Group B.
There could be plenty of drama behind them on Tuesday night, but Barcelona come into this match with top spot and a place in the last 16 already secured.
Indeed, Ernesto Valverde's side were the first to reach the knockout rounds in the entire competition, making light of a difficult group which also contains Inter Milan and PSV Eindhoven in addition to Tuesday's opponents.
Records have tumbled in the process too; Barca have now won their group an unparalleled 20 times, including in each of the last 12 seasons - another record - and if they avoid defeat to Spurs then it would be the 12th time that they have progressed through the group stage without losing a game.
The five-time champions of Europe have dropped only two points in the competition so far, and even their draw at San Siro was enough to seal their progress before victory over PSV last time out secured top spot.
The triumph over PSV was the first of what is now a four-match winning streak, the most recent of which saw Barca thrash local rivals Espanyol 4-0 on Saturday as Lionel Messi once again stole the show with two stunning free kicks.
Things have not always been going as smoothly on the domestic front this season, although the Blaugrana do still sit top of the La Liga table after 15 games, now three points clear of second-placed Sevilla and five above bitter rivals Real Madrid.
Madrid's success in Europe in recent years has overshadowed Barca's domestic glory, and that will have only increased their desire to lift the trophy for the first time since 2015.
Attempts to do so last season ended with their remarkable collapse against Roma, although their 3-0 defeat in the Italian capital remains their solitary loss in their last 16 Champions League outings.
Barca also boast a formidable record at Camp Nou in this competition and could equal the longest home unbeaten streak in Champions League history on Tuesday night should they extend their run to 29 matches - a feat only previously achieved by Bayern Munich from March 1998 to April 2002.
Recent Champions League form: WWWDW
Recent form (all competitions): LDWWWW
The task for Spurs is clear, even if it is not simple - match or better Inter Milan's result at home to PSV then they progress, fail to do so and they will be playing Europa League football in the New Year.
To even be in this position looked unlikely less than a month ago, when squandered leads against Inter and PSV left Spurs with just one point from their opening three games and realistically needing maximum points from their next three to qualify.
That is exactly what they have produced so far; having thrown points away against Inter and PSV in the first round of fixtures, they have struck late winners against the same opponents in their last two outings to keep their hopes alive in dramatic fashion.
Both of those games came at Wembley, though, and there is no doubt that Tuesday's match - on paper at least - is the most daunting of the trio for Pochettino's side.
Tottenham's fate remains in their own hands, but they will be working on the assumption that Inter will beat PSV at San Siro, and that only victory at Camp Nou will therefore do.
Barcelona have not lost a Champions League home game since September 2013, though, and have not been beaten at home in the group stages since 2009 - a run of 27 matches - which means that Spurs will need to produce one of the most famous results in their history if they are to get the job done.
Valverde's side have looked far from invincible this season, but Spurs have only won four of their last 17 European away games and have picked up just the one point from their two in the current campaign.
It is a different story across all competitions, where Spurs have won seven of their last nine on the road, including a 2-0 triumph over Leicester City on Saturday evening.
That victory at the King Power Stadium lifted Tottenham back up to third in the Premier League table and six points behind leaders Liverpool, so they remain right in the mix to qualify for this competition again next term.
However, they will not want Tuesday night to be their last taste of Champions League action until next September at best, and winning at Camp Nou is now the only way to guarantee that will not be the case.
Recent Champions League form: LLDWW
Recent form (all competitions): WWWLWW
Luis Suarez and Messi were also on the scoresheet against Espanyol, and the latter is the joint-top scorer in the Champions League group stages this season.
It could be a landmark game for Sergio Busquets, meanwhile, with the Spaniard set to make his 100th Champions League appearance for the club.
Barcelona possible starting lineup:
Ter Stegen; Semedo, Pique, Lenglet, Alba; Rakitic, Busquets, Vidal; Messi, Suarez, Coutinho
Tottenham possible starting lineup:
Lloris; Walker-Peters, Alderweireld, Vertonghen, Davies; Winks, Dier; Son, Alli, Eriksen; Kane
Head To Head
These two sides had only met twice before this season, with those matches coming in the semi-finals of the 1981-82 Cup Winners' Cup.
Barcelona ultimately came out on top in that tie en route to lifting the trophy, recording a 1-0 win on Tottenham's only previous visit to Camp Nou after a 1-1 draw at White Hart Lane.
The Spanish outfit ran out 4-2 winners in the reverse fixture on matchday two, with Messi starring once again at Wembley.
We say: Barcelona 3-1 Tottenham
Tottenham have no choice but to go for this one, and that could open up space for Messi and co to do some damage at the other end. The visitors have done well to give themselves hope going into matchday six, but Barcelona at Camp Nou is likely to be a bridge too far for them.