The striker picked up two yellow cards in two minutes late on as the game boiled over at times.
Referee Willie Collum handed out eight bookings and the red card and left the field to a chorus of jeers.
Dunfermline had the first chance after seven minutes when Crawford was given far too much room at the edge of the box, but he drilled his shot too close to Mark Brown.
Darren Dods then made a great blocking tackle on Gary Mason when the midfielder looked set to score after being put through by Greg Ross.
From Scott Muirhead's resultant corner, Phil McGuire headed wide as Dunfermline pressed for an early opener.
Ian Black responded as he cleverly sold Muirhead a dummy in midfield before unleashing an ambitious 30-yard shot which Dorus de Vries had to deal with.
Barry Wilson tried one outrageous effort when he attempted to beat de Vries with a 40-yard free-kick which flew high into the stand behind the goal.
Crawford had another glimpse of goal after half-an-hour when Jim Hamilton headed on a long through ball from McGuire but Ross Tokely made a superb last-ditch tackle to send the ball spinning for a corner.
The game erupted early in the second half after referee Collum awarded a free-kick after Wilson and Young tussled on the touchline.
Muirhead got involved and shoved Wilson to the ground but, incredibly, the referee took no action other than to book the Inverness player.
Moments later, it took an instinctive save from de Vries to keep out a Wilson shot after a mistake by Darren Young.
There was more bad blood when Black and Mason clashed in the centre circle. Players from both sides jumped in and de Vries even joined the melee and was booked for his part, along with Black.
Crawford's bookings - firstly for dissent and then for a late tackle on Richard Hastings - left Dunfermline with ten men late on.