The former Chelsea defender, on loan from Burnley, was sent off in the 64th minute of a drab match for a second bookable offence.
Sinclair had already been cautioned for dissent when he brought down Brighton full-back Adam El-Abd.
Sinclair risked talking himself into further trouble by walking towards the linesman to protest over his first booking once he had received his marching orders.
Huddersfield coped well without him to make it two draws and a win in Murphy's temporary reign since the sacking of Peter Jackson.
Both teams are in mid-table with little to play for and it showed.
Brighton gave another lacklustre performance at Withdean, where they have now failed to score in five of their last seven matches.
It could have been different if Jake Robinson had demonstrated the lethal finishing he produced when he scored a hat-trick at Huddersfield earlier in the season.
He wasted a great chance to put Brighton ahead in the 48th minute. Alex Revell set him up 12 yards out after Huddersfield keeper Matt Glennon could only parry El-Abd's shot but Robinson blazed over the bar.
He spurned another opportunity eight minutes later dragging his shot wide of the far post after Dean Cox chipped him into space inside the area, with Huddersfield looking for offside.
Skipper Jonathan Worthington had Huddersfield's best effort shortly before Sinclair's departure reduced them to ten men.
The combative midfielder worked his way through three challenges to unleash an angled drive which was acrobatically palmed over his own crossbar by Brighton's on-loan goalkeeper Scott Flinders.
Sinclair had already been cautioned for dissent when he brought down Brighton full-back Adam El-Abd.
Sinclair risked talking himself into further trouble by walking towards the linesman to protest over his first booking once he had received his marching orders.
Huddersfield coped well without him to make it two draws and a win in Murphy's temporary reign since the sacking of Peter Jackson.
Both teams are in mid-table with little to play for and it showed.
Brighton gave another lacklustre performance at Withdean, where they have now failed to score in five of their last seven matches.
It could have been different if Jake Robinson had demonstrated the lethal finishing he produced when he scored a hat-trick at Huddersfield earlier in the season.
He wasted a great chance to put Brighton ahead in the 48th minute. Alex Revell set him up 12 yards out after Huddersfield keeper Matt Glennon could only parry El-Abd's shot but Robinson blazed over the bar.
He spurned another opportunity eight minutes later dragging his shot wide of the far post after Dean Cox chipped him into space inside the area, with Huddersfield looking for offside.
Skipper Jonathan Worthington had Huddersfield's best effort shortly before Sinclair's departure reduced them to ten men.
The combative midfielder worked his way through three challenges to unleash an angled drive which was acrobatically palmed over his own crossbar by Brighton's on-loan goalkeeper Scott Flinders.