It ended 2-2 after extra-time, and the penalty shoot-out went to sudden death after ending 4-4.
United goalkeeper Gareth Howells made it 5-4, and Blackpool's top scorer that season - Dave Bamber - shot wide, sending Torquay up.
In 1988 United, then under Cyril Knowles, lost out against Swansea City in the play-offs.
They suffered a similar fate in the play-off semi-final against Preston North End in 1995 and in the final at Wembley in 1998, when a penalty earned Colchester United a 1-0 win.
And then there was the Exeter City catastrophe last season.
At home in the play-off semi-final second leg, 20 minutes left to play and 3-1 up on aggregate, they then conceded four goals to lose 5-3.
The nightmare lingers long in the memory.
It's not been all bad
Torquay mourn dropping out the Football League in 2007
When United were relegated two seasons ago, most fans feared the worst - that it just would not be the same, not being in the Football League any more, especially after an uninterrupted run of 80 years.
In fact, it has been quite good fun.
United have been battling at the top of the table, not at the bottom, which is nice.
But should Sunday prove to be their final day in the Blue Square Premier, that would be even better.
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