Santos had to work hard to defend their lead against a lively Avai side in the absence of playmaker Paulo Henrique Ganso, whose knee operation last month has put him out until next year.
Six minutes from the end, the 18-year-old Neymar began the move that ended with Marcel scoring to give Santos a two-goal cushion before Valber pulled one back for mid-table Avai in stoppage time.
A fourth successive win put Santos on 30 points after 17 games, eight behind leaders Fluminense who were held 1-1 at home by Palmeiras on Wednesday and four below second-placed Corinthians.
Santos and Corinthians have a game in hand over Flu and fourth-placed Botafogo, who also have 30 points.
Neymar picked up his third yellow card of the championship against Avai, however, and will miss Sunday's match away to title holders Flamengo at the Maracana.
This will be a relief to troubled Flamengo, who went down 1-0 away to Cruzeiro in new coach Silas's first match in charge on Wednesday and are 15th with 21 points, only four above the relegation zone.