Venezuela defender Luis del Pino received his second yellow card for a bad tackle in the 75th minute.
Peru had most of the scoring chances but couldn't capitalize on them before a small crowd at the Arena Gremio, although Jefferson Farfan had a second-half goal disallowed for offside.
"We are disappointed with the result because we deserved the victory," veteran Peru striker Paolo Guerrero said. "We had our chances but made too many mistakes in front of goal."
The result left the teams tied in second place in Group A, two points behind host Brazil, which opened with a 3-0 win over Bolivia on Friday in Sao Paulo.
On Tuesday, Peru faces Bolivia, while Venezuela plays Brazil.