Pompey midfielder Andre Dozzell went closest to a winner at St Mary's, striking the Saints' crossbar during an impressive first-half performance from the visitors.
Will Still's hosts had the better of the second period but offered little going forward as the match fizzled out.
Portsmouth are ninth in the table with eight points from five matches, with Southampton two points behind in 15th position.
Saints were relegated to the second-tier Championship in April after one season in the Premier League.
"It was a bit of a stop-start game," Southampton's Still told the BBC.
"There were a lot of free-kicks, throw-ins, goal kicks and it just sort of flattened things to be honest.
"But maybe that was what they wanted, they probably came here for that and got what they wanted so fair play to them for that."
Portsmouth head coach John Mousinho said he was proud of his team, adding that he wanted to use the result "to springboard ourselves to bigger and better things".