The Sao Paulo had team won the away leg 1-0 last week and advanced to the final after playing out a stalemate in soggy conditions that diminished the quality of football from both sides.
Santos went into the game knowing they needed to score to keep the tie alive and enjoyed a majority of the possession, but Corinthians packed their defence and made it difficult for the visitors to break them down.
The pick of the early chances fell to Corinthians when Alex's free kick forced Rafael to make a fine fingertip save, but Santos stunned the home fans when they took the lead in the 35th minute to level the tie.
Gifted striker Neymar, considered by many to be the best player in the country, had been given little chance to run at the Corinthians backline but when the 20-year-old finally found some space, he was able to gave Santos the lead.
Ten minutes before the break, he pushed the ball out wide to Alan Kardec and kept running to be on hand to bundle the ball into the net after Borges had prodded Kardec's cross onto the post.
Backed by a capacity crowd, Corinthians recovered from the setback and equalised just two minutes into the second half when Alex swung over a free kick from the left and the ball fell to an unmarked Danilo, who coolly sidefooted it into the net.
Santos pushed for a second goal but rarely troubled the well-organised Corinthians defence.
The draw means Corinthians have not lost a home match in the Copa Libertadores all season and have conceded just three goals in 12 games.
"Our players deserve it, the fans deserve it, the management team deserves it," said Danilo, who won the South American equivalent of the Champions League with Sao Paulo in 2005.
"But we know that we've not won anything yet. Our feet are still on the ground."
Corinthians will face either six times champions Boca Juniors of Argentina or Universidade de Chile in the final. The teams play their second leg in Santiago on Thursday with the home side looking to overturn a 2-0 deficit.