Goals from substitutes Joe McNerney and Ibrahim Meite were enough for Harry Kewell’s side to consign Steve Evans’ charges to a 2-0 defeat at Evans’ former club.
It dropped Mansfield down to ninth, out the play-off places on goal difference.
The Stags should have taken the lead just three minutes into the match when Jimmy Spencer’s pass found CJ Hamilton free in the area.
Hamilton deftly sidestepped keeper Glenn Morris but his shot towards an unguarded net lacked power and allowed Crawley defender Josh Yorwerth to rush back and clear.
At the other end, home striker Jordan Roberts had space and time 20 yards out but his wild effort not only cleared the crossbar but also the roof of the visitors’ stand behind it.
In the 21st minute, Mark Randall burst into the Mansfield area and looked to have been brought down from behind by Will Atkinson but referee Gavin Ward waved away the protests.
Although Alex MacDonald covered acres of ground trying to create chances for Mansfield, his balls forward could not find a way past the defensive pairing of Yorwerth and Mark Connolly.
And at the other end of the pitch Conrad Logan did not have a single save to make in a half lacking in goalmouth action.
The second period was following a similar pattern until Crawley took the lead on the hour mark.
Defender Joe McNerney, who had come on as a second half replacement for the injured Connolly, headed home Roberts’ cross after Mansfield had only half cleared a corner.
Morris did have to be on his toes in the 73rd minute when MacDonald found space 15 yards out, but he shot straight at the keeper’s midriff.
And Mansfield conceded a second in extra time when Meite outpaced the Stags defence and beat Logan with a low shot.
CRAWLEY (3-4-1-2): Morris: Connolly (McNerney 45), Yorweth, Lelan; Young, Randall (Bulman 90+1) Payne, Evina; Smith; Roberts, Boldewijn (Meite 88).
Subs not used: Mersin, Lewis, Doherty, Verheydt.
MANSFIELD: (4-4-2): Logan; White, Bennett, Diamond, Hunt (Pearce 76); Anderson, MacDonald, Atkinson, Hamilton (Butcher 68); Spencer (Angol 59), Rose.
Subs not used: Olejnik, Digby, Mellis, Sterling-James.
REFEREE: Gavin Ward.