Adrian Forbes' early strike ensured that Swansea signed off league football at the Vetch Field with a win.
Adrian Forbes celebrates the last ever league goal at the Vetch
The Swans move to a new stadium next season and the win over Shrewsbury still leaves the Welsh side with a chance to grab automatic promotion.
Lee Trundle threaded a pass across the box for Forbes lurking on the right, who shot into the top-right corner.
Shrewsbury were on top for long periods and it needed goalkeeper Willie Gueret to pull off some outstanding saves.
Swansea: Gueret, Ricketts, Monk, Iriekpen, Gurney (Austin 45), Forbes, Martinez, O'Leary, McLeod (Thorpe 75), Connor (Britton 60), Trundle. Subs Not Used: Murphy, Tate.
Goals: Forbes 8.
Shrewsbury: Hart, Wilkinson, Tinson (Smith 61), Aiston (Lyng 79), Whitehead, Challis, Cowan, Ashton, Edwards, Street (Adaggio 72), Langmead. Subs Not Used: Howie, O'Connor.
Ref: R Olivier (W Midlands).