Corinthians dominated proceedings at home but were not able to capitalise, with Roger Guedes also failing to convert from the penalty spot with the interval approaching.
It would have been a deserved lead for the Timao after a positive opening 45 minutes, but Guedes was brilliantly denied in the 43rd minute by Agustin Rossi, who guessed correctly and quickly reacted to save.
The home side's best chance in open play fell to Giuliano after a mazy dribble into the penalty area from Willian in the 46th minute, but Marcos Rojo scrambled to quell the danger.
With Exequiel Zeballos and Dario Benedetto struggling to have a tangible impact, coming back to Buenos Aires for the second leg with parity intact is a positive for Boca, after also failing to defeat Corinthians in their two Group E games.