The biggest chance came from Dusan Tadic, who missed the target from inside the six-yard area.
Southampton dominated throughout but were unable to find a way past Lukasz Fabianski.
Saints dominate first half
Swansea lined up the new season in a 4-3-3 formation, with Wayne Routledge at the right and Jordan Ayew on the left either side of Tammy Abraham.
Southampton returned to a 4-2-3-1 shape used last season, with Nathan Redmond operating on the left, James Ward-Prowse from the right and Tadic behind Manolo Gabbiadini.
The first chance of the game came within two minutes, as Gabbiadini’s glancing header at the near post clipped off the top of the crossbar.
Southampton came out the stronger side and Tadic should have put the hosts in front inside four minutes, shooting wide from inside the six-yard area with the goal gaping.
It was an encouraging start from the hosts, which will have pleased fans at the ground who only saw their side score 17 Premier League goals at home last season, only relegated Sunderland had fewer.
Swansea’s first chance came through Abraham, who met Routledge’s cross with the goal at his mercy but was unable to find the corner but instead his header flew just wide.
Ward-Prowse then had a deflected shot tipped over the bar by Fabianski, as Southampton began to turn up the heat on that Swansea defence, after a flurry of half chances shortly followed Ward-Prowse’s effort.
Redmond was key all afternoon in Southampton’s attacking play, picked up some wonderful positions in transition especially and had a chance after 23 minutes from range just fly over the bar, while Ward-Prowse had his effort held by Fabianski.
Saints manager Mauricio Pellegrino was hired partly to improve aesthetically on the football being played last season, and so far the fans will have few complaints as their side looked sharp offensively.
Second half followed suit
Swansea had the first chance of the second half, as Abraham turned well inside the box before shooting, the rebound fell to Leroy Fer but his volley towards an empty net was skewed wide.
Southampton responded through Gabbiadini, chasing onto a Tadic through ball before cutting inside on his left foot and curling a strike inches wide of the post.
The home side continued to dominate, but created very few clear-cut chances while Swansea sat deep and hoped to counter-attack even with very little pace in their side.
Saints have never won a home game on the opening weekend of a Premier League season (D5, L4), and this afternoon began to look like that run would continue as the game approached the final third.
The home side rung the changes, bringing on Charlie Austin and Sofiane Boufal in an attempt to finally break through a Swansea defence that looked a polar opposite to the one that conceded 70 goals last season.
Fabianski was forced into a stunning save, tipping Tadic’s shot from 30 yards round the post, just seconds before Maya Yoshida somehow missed the target from the resulting corner.
Yoshida was unmarked at the back post following Oriol Romeu’s flick-on but he blazed his header over the bar.
Tadic then curled an effort over the bar as Swansea brought Kyle Bartley on for Abraham, manager Paul Clement indicating his side were clinging on for a very valuable point, which they were able to bring back to South Wales.