Marco Mathys' strike 10 minutes from the end gave the already-eliminated Swiss side the win but Kuban Krasnodar's draw with Valencia means Michael Laudrup's men advance
Swansea City ensured its place in the last 32 of the Europa League despite losing 1-0 away to St Gallen on Thursday.
Michael Laudrup's men went into their final Group A encounter knowing that a draw would be enough to see them progress to the knockout stages.
Even with a slip-up, only a three-goal swing and a victory for Kuban Krasnodar over Valencia would have been enough to see the Welsh club eliminated from the competition.
St Gallen - playing for nothing more than pride - struck the winner 10 minutes from time, as Marco Mathys found the net from close range.
Swansea could not respond, but the result was made immaterial by Valencia's 1-1 draw with Kuban in Spain.
Wilfried Bony returned from his hamstring injury to solve Laudrup’s striker problems, the Ivorian coming in as part of six changes made by the visitors from their 1-1 draw against Hull City, with Wayne Routledge and Alejandro Pozuelo also included.
Chances proved few and far between for most of the first half, with the two sides reduced to speculative efforts from long range.
However, Swansea perhaps should have taken the lead after 32 minutes when Lamah found space on the edge of the penalty area only to fire narrowly off target.
Bony went close immediately after the halftime interval, but Swansea had goalkeeper Gerhard Tremmel to thank for keeping the team on level terms a few moments later as he produced a fine save to deny Mathys.
Fortune favored Swansea for much of the second half, with only the woodwork preventing Sebastien Wuthrich's free-kick from finding the net.
Defender Chico Flores went off with an injury for Swansea shortly after that scare, and the Welsh side's defense looked to have finally been breached when Neil Taylor bundled the ball into his own net under pressure, however, the goal was ruled out for a push by Wuthrich.
Swansea's defensive efforts became more desperate in the closing stages, Jose Canas clearing a Mathys header off the line, but the Swiss club finally snatched a deserved victory when the same player volleyed home Wuthrich's left-wing cross.
A tense finale followed for Swansea, but as news of Kuban's draw in Valencia filtered through, its progress was confirmed.Follow GOAL.COM USA on