Ross Dickson had given Shotts the lead after 25 minutes before Shettleston were reduced to 10 men in the second-half.
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The red card came in the most unlikely of circumstances, with less than 20 minutes remaining, Whyte went behind one of the goals to urinate - but when he returned to the pitch, was given his marching orders.
The duo play in the West of Scotland Super League First Division, the second-highest level of junior football in the western region of Scotland.
Shettleston have produced a number of notable players including Scottish international Campbell Forsyth as well as former Manchester United manager Tommy Docherty.