Motherwell missed several chances before the Scottish Premier League clash changed in the 63rd minute when Paul Quinn was sent off for a last-man foul.
The visitors looked to be comfortably holding on for a point until the ball broke for Bryson to net from close range in the 88th minute.
John Sutton had passed up the best of the opportunities as Motherwell failed to find reward for some impressive build-up play.
But Killie’s resilience saw them go three points clear in third place as Bryson added to his winner at Tynecastle two weeks ago.
Motherwell suffered a blow before kick-off when skipper Stephen Craigan failed to recover from a groin injury. He was replaced by David Clarkson, who played on the left of a four-man midfield, with stand-in captain Keith Lasley dropping to right-back and Quinn moving inside.
Motherwell made a lively start and only Frazer Wright’s sliding challenge stopped Sutton converting a Steven McGarry cutback, before Alan Combe held Stevie Hammell’s 30-yard free-kick towards the top corner.
Kilmarnock had their first chance in the 12th minute after Stephen Hughes slipped while clearing, but Graeme Smith comfortably held after Conor Sammon had cut inside and shot.
Chris Porter slotted home in the 14th minute after Clarkson slipped the ball through but the offside flag was quickly raised.
The home side were forced into a change in the 17th minute as Simon Ford limped off for James Fowler to come on at right-back.
Smith made a fine double save moments later after Sammon had headed on Mehdi Taouil’s lofted ball forward.
The Motherwell goalkeeper first beat away Bryson’s volley towards the far corner before holding Danny Invincibile’s first-time follow-up.
The visitors regained the ascendancy and Sutton could not direct a free header on target from McGarry’s near-post corner. Sutton had another good chance after Jamie Murphy’s cross took out Combe but the striker could not guide his header underneath the bar.
Smith appeared to be barged over by Sammon after Killie broke but Motherwell cleared and Sutton passed up another opportunity when he opted to dummy Clarkson’s ball across the box.
Murphy was causing Jamie Hamill problems on the right wing and Combe turned the teenager’s powerful strike past the near post.
Sutton waited less than four minutes of the second half for his next chance after Murphy found him space on the edge of the box. His shot beat Combe but a deflection slowed the ball down and Wright cleared off the line. Motherwell kept the pressure on but Combe held McGarry’s 20-yard drive.
The chances dried up and the match changed when Quinn brought down David Fernandez as the Spaniard ran through on goal.
The Motherwell defence had been caught square by Sammon’s lob over the top and Quinn had no option but to make the challenge just outside the box, earning a red card from referee Alan Muir.
Taouil blasted the free-kick into the wall before Sutton was sacrificed for Bob Malcolm to come on in central defence.
Motherwell were initially forced back and Smith got down well to save Taouil’s bouncing 30-yard strike.
The more defensive-minded Marc Fitzpatrick replaced Clarkson as Well looked to protect their makeshift back four.
They did so successfully for the bulk of the last quarter, keeping Kilmarnock well away from the final third. The visitors may even have sneaked victory had Porter’s pass to an unmarked Fitzpatrick been more accurate after a Murphy-led counter attack.
But Killie got a break when Hammill’s shot from the left was defletced into the path of Bryson at the far post and the Killie midfielder slid the ball past Smith.