The 22-time Brazilian champions last lifted the trophy in 2011, while the visitors have reached the final on two separate occasions but are yet to win on the biggest stage.
Santos had to go through qualifying to reach this year's Copa Libertadores, as they took on Argentinian side San Lorenzo over two legs in the third round.
Ariel Holan's side picked up a 3-1 win in the first leg in Buenos Aires, as Lucas Braga and Marinho got on the scoresheet before Angelo Gabriel netted a crucial third goal deep into added time to take a two-goal lead into the second leg.
They then took a 2-0 lead on the night at home through Marcos Leonardo and Para, and goals from Franco Di Santo and Angel Romero pulled the aggregate scoreline back to 5-3, but the visitors were unable to find the two more goals that they required.
That followed a 3-2 aggregate victory over Deportivo Lara in the second round of qualifying, as Vinicius Balieiro, Kaiky Fernandes and Yeferson Soteldo all got on the scoresheet over the course of two legs.
The Peixe currently sit second in their Campeontao Paulista group, but Holan's priority will firmly be on the continental cup, as his side look to cruise through the group stage.
They take on Barcelona SC in the first game, after the visitors lifted the Ecuadorian Serie A last season.
The away side qualified for the Copa Libertadores after lifting the domestic trophy for the 16th time in the club's history, and the first since 2016.
Fabian Bustos's side have had a strong start to this domestic campaign too, currently sitting top of the Ecuadorian top flight after nine games.
They were forced to settle for a point against Mushuc Runa last time out, as a Michael Hoyos brace levelled the game after the hosts took a two-goal lead inside the first 10 minutes.
Bustos's men will now turn their attention to the South American scene, as they look to secure a first Copa Libertadores title, starting with what would be an important victory on Tuesday to kickstart their bid to reach the knockout stage.
Holan made two changes to his side for the second leg against San Lorenzo, as Madson and Yeferson Soteldo came into the lineup in place of Lucas Braga and Vinicius Balieiro.
Both players will be pushing for returns to the starting side, after they both found the net in the victory over Deportivo Lara in the second round of qualifying.
Barcelona SC are expected to remain without right-back Pedro Velasco, who has missed the last five games with an Achilles tendon rupture.
Midfielder Gabriel Marques is yet to feature this season due to a ligament rupture.
Carlos Garces is expected to lead the line, having started eight of their nine league matches so far this season.
He will be supported by the attacking threat of Damian Diaz, who has registered four goals and an assist in nine games from midfield.
Santos possible starting lineup:
Paulo; Madson, Peres, Fernandes, Para; Alison, Jonatan; Marinho, Pirani, Braga; Leonardo
Barcelona SC possible starting lineup:
Burrai; Castillo, Leon, Riveros, Pineida; Torres, Pinatares; Hoyos, Diaz, Martinez; Garces
We say: Santos 2-0 Barcelona SC
Despite their relatively differing fortunes in domestic action this campaign, we see Santos having too much for the visitors on Tuesday.
The Brazilian giants battled hard to get through qualifying, and have plenty of experience on this stage which we feel will fire them to an important victory.
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