The Irishman opened the scoring with a first-half header before doubling the away side's advantage five minutes after the restart.
He completed his hat-trick by capitalising on an error from Hearts goalkeeper Jamie McDonald before Marius Zaliukas scored a late consolation for the home team.
The victory moves Kilmarnock up to third in the league table and leaves Hearts without a home win in the league since the opening day of the season.
Kilmarnock started with the same eleven that had beaten St Mirren 3-1 last Saturday, with Sheridan supported by Gary Harkins, Danny Racchi and James Dayton in a 4-2-3-1 system.
Hearts boss John McGlynn named an unchanged line-up from the team that defeated Livingston to advance to the quarter-finals of the Scottish Communities League Cup.
That meant a fourth successive start for Callum Paterson as the team's lone striker, the 17-year old cementing his place with a brace against Dundee United last Saturday, and he was supported by Scott Robinson, Arvydas Novikovas and Andrew Driver.
The fresh-faced forward line almost got their team off to the perfect start after two minutes. Robinson squared to Paterson whose flicked through pass for Driver, sprinting in behind, just had a little too much pace as the winger was beaten to the ball by Kyle Letheren.
At the other end, Dayton's free-kick was inches away from finding the stretching Liam Kelly at the back post.
Following a free-kick of their own, Hearts then forced the game's first shooting chance but Novikovas sliced high over the bar from 12 yards after he was found free in the box by a Ryan McGowan cut-back.
Novikovas almost atoned for that miss as his cross looked certain to find Paterson at the back post, but the ball was deflected wide by a lunging block from Michael Nelson. Paterson then headed over from the resulting corner.
Hearts could not score when in the ascendancy and they found themselves a goal down on 32 minutes. While right-back McGowan was receiving treatment on the sidelines, Dayton attacked Ryan Stevenson as the midfielder covered the vacant defensive position.
The winger dropped his shoulder, got a yard on Stevenson and his clipped cross into the centre was headed into the far corner by Sheridan.
Hearts started the second half determined to get back into the game, with Paterson shooting wide from the edge of the area a minute after the restart, but they found themselves 2-0 down on 50 minutes.
Sheridan appeared offside when Manuel Pascali's ball over the top was first played, but the linesman's flag stayed down and Sheridan kept his cool, running into the box on the right-hand side before opening his body up and sidefooting past McDonald.
On 62 minutes, Kilmarnock had the game wrapped up and Sheridan had his hat-trick. The striker was in the right place to tap home after McDonald had fumbled a free-kick cross by Racchi, and the Irishman looked almost bashful as he took in the adulation of the ecstatic away support.
Hearts pushed forward and never gave up hope of at least netting a consolation, Letheren denying them on two occasions after Paterson had missed a great chance inside the penalty area.
The keeper then pushed away a John Sutton shot from the edge of the box before tipping a deflected Medhi Taouil effort over the bar.
From the resulting corner the home side got themselves on the scoresheet, Zaliukas rising highest to power Danny Grainger's cross into the back of the net.