The game looked to be petering out a 0-0 draw before the Stags' defence switched off and allowed Trotman a free close-range header to put away a long Conor Hourihane free-kick.
Stags had lost three of their back four and their goalkeeper for the game, but this was still the first goal they had conceded in 276 minutes of football.
However, their lack of a goal in 338 minutes underlines their current problems as they went a fifth game without victory.
Mansfield dominated a first half they began in style with Argyle pinned back in their own half for much of the first half-hour.
Clucas looked a certain scorer in the 15th minute when he met a low Lee Beevers cross at the near-post only to see keeper Luke McCormick make a brilliant reaction block from six yards.
Clucas twice missed the target with other chances while big Matt Rhead headed over and saw Maxime Blanchard produce a timely block as the striker tried to put away a low Clucas cross.
Stand-in home keeper Liam Mitchell finally had something to do in the 29th minute as Romuald Boco shot straight at him, then Lewis Allesandro headed over in the 35th minute as the half ended goalless.
Mitchell did have to beat away an early Boco shot after the break before the Stags again took the game by the scruff of the neck only to see Daniel fail to turn a low Rhead cross into an empty net and Rhead and Ritchie Sutton fail to convert headed chances.
In the end they paid the price as Argyle stole it at the death.