Sam Surridge scored his seventh goal of the campaign with a blistering drive before Connor Smith saw red for two bookings.
Mark Randall volleyed home an equaliser on the stroke of half-time and there was still time for referee Brett Huxtable to send off Omar Sowunmi for a last-man challenge.
The Glovers battled valiantly in the second half but it wasn’t enough as substitute Thomas Verheydt nodded in a winner on 87 minutes.
Olufela Olomola was granted his first start since the beginning of December, partnering fellow young loanee Surridge up front.
Manager Darren Way’s other change to the team that suffered a loss in their last game of 2017 saw Ryan Dickson return from illness.
With skipper James Bailey out of action for up to three months, Connor Smith had another chance to impress in central midfield and it was the Irishman who played a key part in the game’s first attempt on goal.
His interception deep into Crawley territory allowed Otis Khan to run into the box. The tricky wide man teed up Surridge but Josh Yorwerth got his body in the way of the youngster’s shot.
Town playing the ball quickly and with purpose; Tom James almost released Jake Gray with an excellent slide-rule pass, however the two-time goalscorer over the festive period was thwarted by the sliding body of stopper Glenn Morris.
The visitors’ goalkeeper received a booking moments later for carrying the ball outside the area, presenting Khan with a free kick in a very good position, though he could only curl over.
Then came the first goal the hosts thoroughly deserved. Breaking from a Crawley corner, Olomola sped down field with Connor Smith and Surridge in support.
Searching for the duo in the box, the Southampton man’s cross-cum-shot cannoned off the crossbar into the latter’s path and he dispatched with a powerful strike through Morris’ hands.
Things began to get pretty feisty from the away side’s point of view resulting in ex-Glover Lewis Young and centre-back Yorwerth receiving bookings – the Red Devils’ third and fourth yellows in the first period.
Town had been pretty squeaky clean on the discipline front but that changed when Connor Smith was sent off for a second bookable offence.
The former Plymouth Argyle was previously carded on 24 minutes before an innocuous challenge on Yorwerth saw him dismissed by referee Huxtable.
Playing against a man less seemed to lift Crawley and with their first effort on goal, they equalised.
Just before half-time, Jordan Roberts’ cross was put in the far corner by a looping acrobatic volley from Randall to leave the home crowd stunned.
They were left even more so when Sowunmi joined Connor Smith in the changing room.
Roberts hit the deck after being lightly stroked by the big centre-back, who was sent off for ‘denying a clear goalscoring opportunity’.
As expected, Crawley came out all guns blazing in the second half due to their two-man advantage and Artur Krysiak needed to be alert to tip away Enzio Boldewijn’s skewed delivery.
The Dutchman then went on a mazy run which led to Randall flashing an effort just past the post.
The Glovers did have their own spells where they threatened; Surridge causing a nuisance but seeing a shot blocked while Tom James sent a free kick well wide.
Amazingly, official Huxtable didn’t award a second caution for Yorwerth. First he hauled down Olomola – free kick awarded – before wrestling Surridge to the ground; nothing given.
The effort Way’s players put in during the second 45 couldn’t be faulted; they defended gallantly as a unit and broke well despite their lack of numbers.
Bizarrely, the last 10 minutes were delayed due to a drone over the stadium. Play eventually resumed and Crawley grabbed a late winner with Verheydt rising highest to head in Jimmy Smith’s cross.
Town had one more chance to salvage something from the contest but Morris saved well from James to deny the Glovers a share of the spoils.
Yeovil Town: Krysiak, James, Sowunmi, N.Smith, Dickson, Gray, C.Smith, Worthington, Khan (Mugabi 45), Olomola (Green 76), Surridge (Zoko 82).
Bookings: C.Smith 24, 37, Zoko 90.
Sendings off: C.Smith 37, Sowunmi 45.
Not used: Maddison, Davies, Nelson, Santos.
Crawley Town: Morris, Lelan (Meite 39), Connolly, Yorwerth (Verheydt 74), Evina (Sanoh 62), J.Smith, Bulman, Young, Randall, Roberts, Boldewijn.
Bookings: Roberts 14, Morris 15, Young 31, Yorwerth 32, Randall 38.
Not used: Mersin, Doherty, Clifford, McNerney.