N'Guessan brought his side level after striker Francis Green was sent off in the 69th minute after clashing with Ady Williams in the Swindon area.
The striker was booked for dissent by referee Paul Taylor but carried on arguing and was then shown the red card.
Green ripped off his shirt as he left the pitch and walked straight down the tunnel.
Swindon took the lead after 25 minutes through Andy Monkhouse's first ever goal for the club.
Lee Peacock's header split the Boston defence and Monkhouse rammed a left-footed shot through goalkeeper Andy Marriott's legs and into the net.
Christian Roberts should have doubled Swindon's lead ten minutes later after he and Marriot chased a long ball towards the corner flag. The Robins striker rounded the goalkeeper, but put his shot straight at defender Paul Ellender.
Boston forward Anthony Elding almost made Swindon pay for their missed chances, but his firm header from David Galbraith's cross was saved by Petr Brezovan.
Green had a great chance to pull Boston level before the break when he was put clean through on goal, but his weak shot went straight at Brezovan, who made an easy stop.
Boston left-back Tim Ryan was booked for a foul on Roberts and was quickly followed into the book by Swindon defender Jack Smith, who took the resulting free-kick too quickly.
Green's speculative left-footed shot from 20 yards was easily saved by Brezovan on 47 minutes.
Royce Brownlie then had the chance to double Town's lead after Roberts' cross evaded the Boston defence, but his limp effort failed to trouble Marriott.
After Green was sent off Swindon sat back and appeared happy to settle for a 1-0 win.
Boston huffed and puffed without creating any clear openings, until N'Guessan smashed the ball home from 25 yards with just two minutes remaining.
Swindon came to life after the shock equaliser, but they had left it too late to put pressure on the Boston goal.