Kilmarnock 0 Heart of Midlothian 2
Once again it was a frustrating affair for the home fans in foul weather, as Kilmarnock's failure to convert golden chances haunted them once more.
Indeed, Hearts' opening goal in the 62nd minute came from their first shot of the match.
The blustery, swirling wind and driving rain made conditions difficult, and the first half was the poorer for it.
It was the home side who gained control in the first period and they had the first goal threat in the 31st minute when the wind played havoc with Mehdi Taouil's corner kick delivery, but the Hearts defence was resolute, blocking shots from Frazer Wright, Craig Bryson and Danny Invincibile before they troubled Jamie MacDonald.
The young keeper had an impressive game in difficult circumstances, handling the slippery ball cleanly and calmly and clearing well from foot.
David Fernandez broke clear of the Hearts defence after a rare mistake by Christophe Berra, but the ball appeared to bobble as he shot and the ball flew high and horribly wide.
Killie's best move of the match brought their best chance in the 39th minute. Taouil played a clever pass inside to Garry Hay, whose cross was perfect for Invincibile three yards out, but the Australian headed wide with the goal gaping.
Hearts made Kilmarnock pay just after the hour mark with a great strike from Bruno Aguiar. The Portuguese midfielder was spotted in acres of space 25 yards from goal by Michael Stewart who played the perfect pass and he rifled a superb shot past the diving Alan Combe.
Killie had a chance to equalise straight away, but Allan Russell's half-volley flew wide.
Hearts wrapped up the points ten minutes from time. This time it was down to poor defending rather than silky soccer, as Killie failed to defend a set-piece, leaving Berra free to head the ball across goal to the equally neglected Christos Karapidis who nodded the ball home.
Substitute Willie Gibson almost threw Kilmarnock a lifeline two minutes later, but MacDonald saved his well-hit volley.
Christian Nade had the chance to rub salt in Killie's wounds after a suicidal back pass from Manuel Pascali, but Combe saved with his feet.