Kilmarnock sealed their first win since March thanks
to two second-half goals at Tynecastle.
Hearts were looking to bounce back from Monday's 2-1 defeat at Falkirk
while Kilmarnock approached the game having taken only three points from
their previous five games.
Kilmarnock were first to threaten when David Lilley's left-foot shot
drifted wide of Steve Banks' goal.
At the other end, Laryea Kingston tried to break the deadlock with a
dipping shot that just missed the far post.
The visitors were looking to the pace of Dalglish on the wing to unlock
the Hearts defence.
But, despite several crosses from the former Hibernian player,
Kilmarnock failed to produce a meaningful effort on goal.
As half-time approached, Fernando Screpis missed an excellent chance to
score his first goal for Hearts.
The Argentine, making his full debut for the Tynecastle side, was
played in on goal by Eggert Jonsson, but his tame effort was comfortably
saved by Kilmarnock keeper Alan Combe.
David Fernandez was set up by Dalglish early in the second half, but
his miss-hit shot landed at the feet of Mehdi Taouil, who fired off
target.
Screpis then dispossessed Jamie Hamill and found Kingston, whose fierce
effort from 25 yards drifted just over the bar.
Screpis
continued to be heavily involved in the action and missed another chance
when he sent his snap shot over.
Combe was then called on to prevent an own goal when Murray's
misdirected header crept towards goal.
The breakthrough came 16 minutes from the end when Fernandez sent an
in-swinging corner onto the head of former Hearts defender Grant
Murray, who nodded home. (Right).
Fernandez was booked for his celebration following the goal, but it
mattered little as Paul Di Giacomo (above) clinched victory late on.
The midfielder, who had replaced Allan Johnston, got on the end of
Dalglish's cross and finished well past Hearts keeper Banks.
The victory was Kilmarnock's first away from home in the SPL since
September.
74 mins 
