Jamie Hamill pulled one back for Killie, converting a penalty after Francis Dickoh was ordered off for a challenge on Kieran Agard.
BBC: Sport - Football - Hibernian 2-1 Kilmarnock
2.
The visitors were looking dangerous on the break and Mehdi Taouil picked out Agard on the break, but the on-loan Everton man's effort went wide.
BBC: Sport - Football - Hibernian 2-1 Kilmarnock
3.
Agard headed straight at Stack as the visitors pressed for an equaliser, while Bryson stung the keeper's hand with a fierce drive, but Colin Calderwood's side held firm to claim the points.