Dundee sunk to the bottom of the First Division table after losing a man and the only goal of the game against Partick Thistle.
Thistle's Chris Erskine was brought down in the box by Rab Douglas and the goalkeeper was sent off for conceding the penalty.
Paul Cairney converted from the spot, beating substitute goalkeeper John Gibson with powerful shot into the top corner.
Dundee tried to level matters with Gary Irvine, Gavin Rae, Ryan Conway and Nicholas Riley all having efforts blocked by Thistle keeper Ryan Scully.
Riley had further chances to equalise but the visitors held on for the win.
Dundee: Douglas, Irvine, Lockwood (McKeown 77), McGregor, Weston, Riley, O'Donnell, Rae, Conroy (McCluskey 89), Mcintosh (Gibson 26), Milne. Subs Not Used: Chisholm, Benedictis.
Sent Off: Douglas (25). Booked: Irvine, Riley, Weston, O'Donnell.
Partick: Scully, Paton, Sinclair, Balatoni, Archibald, Cairney, Hutton, Rowson, O'Donnell (Stewart 63), Erskine (Bannigan 80), Elliot (Doolan 78). Subs Not Used: Wightman, Lindsay.
Booked: Sinclair, Erskine.
Goals: Cairney 26 pen.
Ref: Steven McLean