The Southampton skipper handed the home side a 19th-minute lead with an emphatic finish past Swansea goalkeeper Michel Vorm.
The visitors, who were 1-0 winners against St Gallen in the Europa League on Thursday, came close to equalising through Michu and Nathan Dyer.
But the south coast secured three points and hoisted themselves into fourth place when midfielder Jay Rodriguez volleyed past Vorm.
“We’ve been winning games 1-0 before today, which is the sign of a good team,” Lallana told BBC Sport.
“We’ve got another clean sheet today and the back four are playing well while Artur Boruc is making a lot of good saves in goal.
“We’ve got to take it each game as it comes. We’ve won three games on the bounce, we’re confident and building a good, young squad.”
Meanwhile, Swansea manager MichaeL Laudrup felt the Welsh outfit deserved at least a point from their trip to St Mary’s.
“We performed very well. Apart from the first 15 minutes we dominated the game and had lots of chances.
“They got a good goal but the whole of the second half was all about us. We still need too many chances to score.
“After the St Gallen game, I said they deserved a little more. Today, I think we deserved a little more.”
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