Venezia's Alessio Zerbin found the net in his first start since joining on loan from Napoli last year. His initial attempt in the 28th minute was blocked, but he quickly followed up to score from the rebound.
Cameroonian player Jackson Tchatchoua brought the visitors level with just 14 minutes to go, finishing off a swift counterattack with a close-range tap-in.
Verona sat fourth from the bottom, while Venezia was just above them in second to last, three points clear of Monza, who missed a chance to escape the bottom after losing 2-0 to Genoa.
Things could have been worse for Monza if not for the stellar goalkeeping of Stefano Turati, who made a crucial save on a first-half penalty from Andrea Pinamonti.
However, Monza struggled defensively in the air, and Turati couldn't stop Genoa from capitalizing in the second half.
Koni De Winter scored with a header from a well-placed cross in the 61st minute, and then Mexican Johan Vásquez added another with a glancing header from the right side just six minutes before the end.
Genoa climbed up to 11th place.