Elliot, who has been given a tough time by Hearts' fans, left the field to a standing ovation for his display.
The home side could even afford to miss a second-half penalty as they won with room to spare.
Janos Balogh was back in goal for Hearts after suspension and recovering from a hamstring injury sustained in training earlier in the week.
Killie took the lead after eight minutes with the simplest of goals. Mehdi Taouil sent a rather lazy looking cross to the back post but no-one reacted in the Hearts' defence and Danny Invincibile stole in to nod home from six yards.
Hearts hit back immediately and when David Lilley was unconvincing with his clearance, Andrew Driver's quick-fire effort was brilliantly tipped over by Alan Combe.
Elliot then sent David Obua clear, but his 25-yard shot was always drifting wide of target.
Killie were guilty of giving away too many free-kicks at the edge of their area and Hearts equalised midway through the first half after Lilley was guilty of conceding one such foul.
Bruno Aguiar's kick was flicked on at the near post by Ruben Palazuelos and, though Combe pulled off a terrific save, Elliot was brave and alert to stab the loose ball into the net.
The Hearts striker produced a top-notch finish six minutes later when he pounced on a low cross from Lee Wallace to beat Combe with an instinctive strike.
Lilley had a chance to equalise moments later when the ball broke to him at the edge of the box but he could not keep his volley down.
But Kilmarnock never looked comfortable at the back. Obua, having switched wings with Driver, delivered a great cross but Elliot and Aguiar seemed to get in each other's way with the goal at their mercy.
Taouil became the first player to be booked after a lunge on Robbie Neilson on the touchline and he was fortunate only to be shown the yellow card.
Elliot should have completed his hat-trick five minutes from the break when Driver scampered clear on the right and laid the ball on a plate, but he sidefooted his effort tamely wide.
It was 3-1 four minutes after the restart. Elliot out-muscled Manuel Pascali in the six-yard box and played the ball back for Aguiar to score at the near-post.
Hearts were awarded a penalty after 61 minutes when Ryan O'Leary fouled Elliot, but Aguiar's spot-kick struck the inside of the post before bouncing to safety.
Elliot had another chance for a hat-trick after Michael Stewart sent him clear, but his low shot lacked power and Combe saved easily.