© PA Photos
Southampton controlled the early stages of the match and Gaston Ramirez went close with a curled effort from the edge of the box that landed just inches wide of the Swansea post.
The hosts dominated possession for long spells in the first half but almost gifted a goal to the Swans when Ki Sung-Yeung was allowed space inside the box, but his effort was superbly pushed to safety by Paulo Gazzaniga.
Swansea looked a better side as the game opened up in the second half and Angel Rangel was unlucky to see his powerful strike deflected over.
Michael Laudrup's side continued to look the more likely to score in the second period and Wayne Routledge went close with a drilled effort that flew inches over the crossbar.
The St Mary's crowd were angered on the hour mark when Lallana went down under a challenge from Ashley Williams but Andre Marriner rejected the midfielder's claims for a penalty.
However, the home supporters soon changed their mood when the Saints took the lead minutes later as Rickie Lambert found Morgan Schneiderlin, who controlled the ball well before heading past Gerhard Tremmel.
Despite moving into the lead, the Saints gifted Swansea an equaliser when a lack of composure from Maya Yoshida allowed Dyer to collect the ball before easily slotting past Gazzaniga.
The hosts had chances to snatch a winner before full-time with Lambert heading wide from close range, but Swansea were able to hold on for a well-earned point.