Substitute Jay Rodriguez netted his side's other goal of the day seven minutes from time when he benefited from some slipshod defending to tuck the ball beyond Michel Vorm after Jordi Amat and Chico Flores had somehow failed to snuff out a high ball.
Steven Davis set up Lallana for a venomous opener on 17 minutes, his 51st goal for the club and his first since scoring against Reading in April.
Swansea paid the price for failing to take a number of obvious chances with Michu, wearing a skullcap after his head injury against St Gallen in the Europa League, unusually wasteful in front of goal.
Southampton have 14 points, their best start to a season after only seven league matches with Chelsea ahead of them in third spot on goals scored. They are assured of finishing the day in fifth at the very least - even if Tottenham overcome West Ham later.
19' - LALLANA STRIKES: Davis picks out Lallana on the run. And that is a venomous strike high into the net. Saints lead 1-0.
26' - BORUC BRILLIANCE: Rangel throws over a decent cross to the back post. Met by Michu, but Boruc produces a strong arm to make sure the header stays out.
38' - DYER DENIED: Bony picks out Dyer on the run with a lovely backheel, but his shot comes back off the inside post and back out. So unfortunate. Swansea should be level there.
43' - BORUC REFUSES TO BUCKLE: Shelvey finds Dyer on the run. Lovely cross for Bony, but Boruc with another excellent stop for the home side.
75' - WANYAMA GOAL DISALLOWED: Wanyama scores for Southampton, but the referee says there was pushing in the box and the goal has been disallowed.
84' - RODRIGUEZ CLINCHER: Rodriguez earns himself space in the Swansea box before driving the ball into the corner of the net. Canas and Flores all over the place at the back.
Swansea are winless in their last 10 league matches at Southampton, since a 4-1 victory in the old Division Two in March 1953 (as Swansea Town).
Southampton have conceded two goals in their opening seven Premier League matches. At this stage last season they had conceded 20 goals.
Southampton equal their best start to a top flight season after seven matches. They also had a record of W4-D2-L1 in seasons 1980/81 and 1983/84.
Jose Canas receives Swansea's 16th yellow card of the season. Only Manchester United (17) have had more bookings this campaign. Southampton have had the joint-fewest (seven) with Cardiff City (includes Lovren and Fonte bookings today).
TALKING POINT: Where will Southampton finish the season? Like Liverpool, a bit too early to get carried away. They say that luck evens itself out over the season and there is little doubt that the home side were fortunate to extract three points from this one. Can they challenge for the Champions League places? Unlikely, but Europa League qualification is not beyond them. Relegation will not be an issue.
MAN OF THE MATCH
Nathan Dyer (Swansea): Just edges home goalkeeper Artur Boruc courtesy of a vibrant attacking performance. Didn't deserve to be a loser for some of the quality and energy he left on the park.
Southampton: Boruc 8, Clyne 7, Fonte 6, Lovren 6, Fox 6, Wanyama 7, Schneiderlin 7, Lallana 8, Osvaldo 5, Steven Davis 7, Lambert 6. Subs: Rodriguez 8, Ward-Prowse 7, Do Prado 7
Swansea: Vorm 7, Rangel 6, Amat 5, Chico 5, Ben Davies 6, Canas 6, Shelvey 7, Dyer 8, Michu 5, Routledge 5, Bony 7. Subs: Pozuelo 6.
THE MATCH IN A TWEET