Antonio Conte's side are level on 61 points with reigning champions Inter after a largely lacklustre performance which with better finishing would have still been enough for victory on the Venetian Lagoon.
Giacomo Raspadori smacked a shot off the post in the fifth minute at the Stadio Pier Luigi Penzo while Scott McTominay, Giovanni Di Lorenzo and Romelu Lukaku were all denied by smart goalkeeping from Ionut Radu.
And substitute Giovanni Simeone wasted a chance to snatch the three points for Napoli in stoppage time when he blasted over Noah Okafor's pinpoint cross from close range.
Those misses left Napoli with five draws from their last seven league matches, form which has compromised their bid for a second league crown in three seasons.
"I don't think they caused us any problems. There was one team on the pitch that was in charge of the game, and that was us," said Conte to DAZN.
"We did what we were supposed to do today, but when you create so many chances you have to score. And the opportunities they had mostly came from our own errors."
Venezia's performance belied their position in the relegation zone, five points behind Parma who sit just outside the bottom three and drew 1-1 at Monza on Saturday.
The hosts should have scored three minutes before the break when Napoli goalkeeper Alex Meret charged off his line to deny Kike Perez before Amir Rrahmani's desperate goalline clearance from Daniel Fila's follow-up.
Atalanta chance
Napoli's draw presents Atalanta with a great opportunity to draw level with the leading duo in an exciting three-way race for the Scudetto.
Atalanta sit three points off the pace in third as they seek a first home win in Serie A since before Christmas and their first ever league title.
Later Juventus take on rivals Fiorentina in what will be a fiery atmosphere in Florence as Thiago Motta's job is reportedly in the balance after a deeply disappointing season.
Juve need to win in Tuscany, where they will take on old boys Moise Kean and Nicolo Fagioli, in order to reclaim their place in the Champions League positions.
Bologna are one point above Juve in fourth place after a thumping 5-0 win over sixth-placed Lazio, another team bidding for a spot in Europe's top club competition.
Motta insisted on Saturday that he had the full backing of the Juve hierarchy but Italian media have reported that Roberto Mancini is one of the candidates to replace him should results not change.
Bologna's fourth win on the bounce boosted their bid to return to the Champions League after flopping in the competition this year under Vincenzo Italiano, who replaced Motta as coach last summer.
