Saints emerged 2-0 winners from a pulsating, end-to-end encounter at St Mary's, despite spending most of the match on the back foot.
The Swans dominated the majority of play but fell to strikes from captain Lallana and substitute Jay Rodriguez as Saints secured a third successive league triumph.
Southampton also picked up a fifth clean sheet of the season, with goalkeeper Boruc pulling off a string of fine saves to keep the visitors at bay.
"He was incredible," Southampton boss Pochettino said of the Poland international. "He did ever so well, but it just shows we have full trust in his performances and his skill, and also in our other keepers.
"We were able to keep another clean sheet, which was a massive positive for us, but Boruc has our full trust to be our number-one keeper.
"I don't know what happened in the past, but in the eight months I've been here he's been excellent for us.
"There's great competition between the three main goalkeepers and behind in the youth teams, so we're very happy with the great atmosphere between them."
While Boruc was Southampton's best defensive player, goalscorer Lallana shone going forward.
After taking a while to adapt to life in the top flight, the 25-year-old has impressed for Saints this term, leading to suggestions he could follow Rickie Lambert into the England set-up.