The Brazilian Serie A outfit have battled for league form this season and despite four wins in their last five, they only sit 14th in the table.
Their continental form has been impressive, though, and a two-goal home win gives them a great chance of reaching the competition's quarter-finals.
Cesar had defender Emiliano Ciucci sent off in the 63rd minute and less than 120 seconds later, Titi made the most of slack marking to head in Bahia's opener.
Titi scored a free header from four yards after Emanuel Biancucchi's free-kick from the left evaded the Cesar defence.
And substitute William Barbio smashed in from nine yards with 10 minutes to play as Bahia won well.
The second leg will take place in Peru on October 15.
In other first leg last-16 clashes, Ecuador's Emelec left it late before seeing off Brazilian opponents Goias 1-0.
Emanuel Herrera was the hero, nodding home from four yards to end a lengthy goalmouth scramble in the 87th minute.
And Vitoria – also of Brazil – will be happier following a 2-2 draw at Colombia's Atletico Nacional.
Goals to Ednei and William Henrique put Vitoria in front after Daniel Bocanegra had given Atletico a fourth-minute lead.
And although Luis Ruiz levelled from the penalty spot with 24 minutes left, Vitoria's impressive road performance could prove crucial.