Killie were unbeaten last season against Hearts and for manager Jim Jefferies it was a sweet return to Tynecastle where he enjoyed success as a player and manager.
It was the visitors who dominated early possession but when the first opening fell to Manuel Pascali his control let him down after he had found space only eight yards out.
Jefferies had sent out an attacking line-up but an early spate of fouls suggested they fancied they could outmuscle Hearts.
But it was Hearts who threatened next with Christophe Berra flicking Laryea Kingston's corner into the side-netting before the hosts created a glorious chance.
Kingston left Pascali for dead down the right and whipped in an early cross that the stretching Mike Tullberg nudged wide from 12 yards on his home debut.
However, a rash tackle from Jamie Mole on Bryson earned the Hearts youngster a booking and presented Killie with a shooting chance 20 yards out.
And it was to prove costly as Mehdi Taouil clipped a delightful right-foot shot over the top of the wall and into the top corner past the despairing dive of Marian Kello.
Killie continued to dominate proceedings and Hearts' 33rd-minute equaliser was very much against the run of play.
Michael Stewart's shot from the edge of the box was blocked by Bryson but Kingston pounced on the loose ball to calmly slot home from 15 yards.
Back came Kilmarnock with Jamie Hamill cutting inside Jason Thomson and letting fly from a tight angle with Kello gathering comfortably.
And skipper Pascali blew a wonderful shooting chance as he sliced the ball miles wide from 18 yards with time and space on his side.
Hearts replaced the ineffective Mole with Andrius Ksanavicius and he made an immediate impact nudging a pass to Saulius Mikoliunas who fired wide from 20 yards.
Hearts had upped the tempo and Thomson charged down the right to cut back for Kingston whose half-volley flew inches over the bar.
A super pass from Mikolianus played in Kingston and only a fine save by Alan Combe kept Kilmarnock level.
But Killie went ahead again in the 82nd minute thanks to Bryson's goal. He exchanged passes with Donovan Simmonds before running in to the box and slipping a cool low finish past Kello.
Only a fine late save from Kello kept out substitute Gavin Skelton's low drive as Killie eased towards a deserved win.