They had Lee Beevers, skipper Paul Morgan and goalkeeper Alan Marriott all sent off in the closing stages, completing an amazing turnaround to a match they seemed to be winning comfortably at half-time.
Beevers was the first to go, for a second bookable offence in the 78th minute.
But that was nothing compared to the 87th minute incident which saw Morgan and Marriott red carded.
Morgan kicked out at Torquay goal scorer Alan Connell as he shielded the ball out for a corner. Then keeper Marriott ran 20-yards and angrily kicked the loose ball against the fallen Connell.
Referee Paul Melin had little option but to dismiss both men.
By that stage Torquay had turned around a match that they seemed certain to lose.
Lincoln deservedly took the lead in the tenth minute when centre-half Gareth McAuley was unmarked to head home Beever's right-wing cross.
Jittery Torquay made mistake after mistake, and only a full length save by Gulls keeper Andy Marriott stopped Colin Cryan giving Lincoln a two-goal lead just before half-time.
But Darren Garner's 18-yard left foot shot in the 51st minute breathed new life into Torquay.
Connell's clever 65th minute header from a James Sharp cross proved to be the winner and the Devon side were on top by the time Lincoln's discipline disintegrated in the closing stages.