TNS conceded two late goals in their Uefa Cup first qualifying round tie in Sweden after frustrating their opponents for much of the contest.
Tommy Holmes scored into his own net on 77 minutes as he attempted to clear a Fredrik Gustafson cross from the right.
Pär Cederqvist doubled the lead seven minutes later when TNS keeper Gerard Doherty failed to deal with a cross.
The Welsh side showed little attacking intent, and will need to raise their game for the return leg in a fortnight.
TNS were given warning of the home side's ability as early as the fourth minute when Denis Velic hit the crossbar from 20-yards out.
Doherty was on fine form in the first half as he denied Cederqvist, before the striker almost broke the deadlock seconds before the interval with a shot that edged past the post.
TNS struggled to provide lone-striker Jamie Wood with any decent scoring opportunities, and defender Denis Velic went closet when his opportunist shot went over the bar.
Östers IF: Kennfors, Petersson, Gorkss, Thor, Joakim Karlsson, Nouri, Gustafson, Velic, Svensson, Cederqvist, Johansson.
Subs: Green, Bild, Wibran, Axelsson, Sallhag, Soderberg, Ottosson.
TNS: Doherty, Holmes, Alcide, Hogan, Taylor, Aggrey, Ruscoe, Leah, Ward, Wood, Simon Davies.
Subs: Gibson., Toner, McGuire, Beck, Connelly, Wilde, King.
Referee: Oleh Oriekhov (Ukraine).