Luis Mago's 75th-minute dismissal for a second bookable offence gave Peru hope of snatching all three points but a stalemate always seemed the likely conclusion between two evenly matched teams.
Ricardo Gareca's side did have the ball in the net on two occasions, only for offside decisions to deny Christofer Gonzales and Jefferson Farfan either side of half-time.
Both teams now move a point ahead of Bolivia, who lost 3-0 to Brazil in the tournament opener.
Peru appeared to have an early opener when midfielder Gonzales buried a loose ball, but a VAR review showed Renato Tapia to have been offside as he challenged Venezuela goalkeeper Wuilker Farinez.
Christian Cueva and Salomon Rondon failed to take good chances either side of the 20-minute mark, while a poor Farinez punch forced Tomas Rincon to make a crucial block towards the end of a first half blighted by stoppages.
More fluent passages of play after the interval brought only wayward finishing until Peru forward Farfan nodded in Edison Flores' left-sided cross.
The latter had strayed offside before delivering the cross, however, and there was to be no winner even after Mago's second yellow card, with Farinez redeeming his earlier efforts by making a fine close-range save from lively substitute Flores.
What does it mean? More possible from Peru
Having reached the quarter-finals at the Centenario edition in 2016, and as a team that has spent 12 months building on a World Cup appearance, Peru will be especially disappointed not to have taken all three points.
Their level of performance will need to improve if they are to challenge the big nations at this tournament.
Advincula an important outlet for Peru
Venezuela's left side struggled with the mighty task of stopping Peru's barnstorming right-back Luis Advincula, whose pace and positivity gave his team a constant attacking option out wide.
Farinez fortunate to avoid first-half punishment
He did well in the end to earn a clean sheet by denying Flores but other teams in the tournament are sure to bombard Venezuela keeper Farinez with aerial balls after his unconvincing attempts at claiming crosses in the first half almost led to two Peru goals.
Venezuela face hosts Brazil in Bahia on Tuesday as Peru head to Rio de Janeiro to meet Bolivia.