Former Doncaster striker Heffernan started and finished a thoroughly convincing Scottish Premier League victory with two composed finishes at Rugby Park on Sunday.
James Dayton was another stand-out in a slick team performance, with his brilliantly-executed free-kick the pick of the goals.
Dayton helped restore Kilmarnock's lead just before the interval when his cross was turned home by Hibs defender Paul Hanlon.
Hibs handed second-half debuts to experienced striker Junior Agogo, former Aston Villa midfielder Isaiah Osbourne and on-loan Newcastle forward Phil Airey, but their only high point came when Garry O'Connor netted in the 13th minute.
Although O'Connor took his goal in style, even that bright moment owed much to a mistake from the otherwise impressive Kilmarnock defender Ryan O'Leary.
Killie played some free-flowing football with Gary Harkins showing some impressive touches in midfield and in 29-year-old Heffernan they might have found a replacement for his fellow Irishman Conor Sammon.
The Ayrshire side have struggled to win since Sammon left for Wigan in January and Heffernan, whose first start was delayed by injury following his arrival from Sheffield Wednesday, displayed a cool head when he opened the scoring inside three minutes.
Rory McKeown played a high ball in between the visiting centre-backs and Heffernan stroked the ball underneath Graham Stack from 12 yards.
The home side were moving the ball around with confidence but they then shot themselves in the foot.
O'Leary tried to play a difficult pass out of defence but put it at the feet of Lewis Stevenson, who quickly found O'Connor in the left channel.
The striker beat one man and brilliantly lifted the ball over Cammy Bell into the far corner.
Hibs almost returned the gift two minutes later when David Stephens mis-kicked Dayton's low cross straight to the feet of David Silva, but Stack blocked the Portuguese wide man's drive from 16 yards.
Heffernan had a great chance for his second after a brilliant through ball by Harkins. The forward took the ball round Stack but could not keep the ball tight enough to his feet and the goalkeeper recovered to save.
The goalkeeper soon parried Silva's powerful strike on the run from 22 yards.
Kilmarnock continued to make the running and were rewarded in the 41st minute.
Dayton turned Callum Booth one way then the other before firing a low ball across the six-yard box, which was turned into his own net by the stretching Hanlon as he slid in with Heffernan.
Hibs manager Colin Calderwood brought on Osbourne and Agogo for Stevenson and Matt Thornhill at half-time, and they initially looked more of a threat with their new 4-4-2 formation.
But Kilmarnock continued to make the better chances. Dayton curled a free-kick just over the near post after being felled inches outside the box by David Wotherspoon, who soon wrestled Danny Buijs off the ball despite being booked for the earlier foul.
Liam Kelly curled wide after another good Kilmarnock move and Heffernan twice got a shot away after a quick ball up front, neither of them threatening Stack.
And the visitors looked a beaten team following a moment of brilliance from Dayton in the 65th minute.
The midfielder lined up a free-kick 25 yards out after Wotherspoon had bundled over Buijs, and curled a left-footed effort over the wall and into the top corner.
Booth got some respite from his tormenting at the hands of Dayton when he shot straight at Bell before Wotherspoon escaped with a lecture from referee Steven McLean following a trip on Shiels.
Kilmarnock dished out their own punishment within seconds, though, as Dayton found overlapping right-back Buijs, whose near-post cross was stroked into the top corner by Heffernan's volley.
Wotherspoon was unsurprisingly taken off for Airey before the restart but Calderwood could do nothing to prevent Kilmarnock cutting through his defence.
Heffernan had a glorious chance for a hat-trick after clever passing from substitutes Jorge Galan and Dean Shiels presented him with an open goal, but he hit the top of the bar from six yards.