The Welsh side knew that a point would secure their qualification for the knockout stages from Group A but instead a second-half Marco Mathys goal allowed the already-eliminated hosts to bow out on a high.
Nevertheless, the defeat did not prevent the Swans from advancing as Kuban Krasnodar failed to get the victory they required away to Valencia in Spain to stand a chance of grabbing second place.
Spurs thrash Anzhi
Elsewhere, Tottenham Hotspur, who had already qualified before hosting Anzhi Makhachkala at White Hart Lane, made it six wins from six in Group K by beating the Russians 4-1. Roberto Soldado scored a hat-trick, including one penalty, while Lewis Holtby also netted.