Clyde were relegated from Division One Despite beating Dundee after Airdrie's late win at Partick Thistle.
The home side broke the deadlock in the 53rd minute when Andrew Shinnie deflected the ball into his own net.
Clyde made the points safe when Willie McLaren calmly beat Rab Douglas from a tight angle with 13 minutes to go.
And the win appeared to have guaranteed taking the relegation issue to the final day of the season until Simon Lynch's 90th-minute winner for Airdrie.
Clyde: Hutton, Gemmill, Waddell, Higgins, Brown, Lithgow, Ruari MacLennan, Kettlewell (Connor Stevenson 89), Clarke (Winters 72), Tade, McLaren (McKay 90). Subs Not Used: Trouten, Cherrie.
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Booked: Ruari MacLennan.
Goals: Shinnie 53 og, McLaren 77.
Dundee: Douglas, Cowan, Malone, Young, Benedictus, Lauchlan (Williams 89), Efrem, Shinnie, McMenamin, Deasley, O'Brien (Gilhaney 67). Subs Not Used: Posniak, Daquin, Roy.
Booked: Benedictus.
Att: 944
Ref: A Muir
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