Kilmarnock built on their surprising Scottish Communities League Cup final win over Celtic last Sunday with a convincing victory.
Heffernan profited from some clever movement in the 50th minute to open the scoring, firing home at the second time of asking after goalkeeper Darren Randolph had stopped his first effort.
The striker doubled his advantage with a 61st-minute penalty after James Fowler's shot was blocked by Tom Hateley's hands.
Motherwell were lacking in creativity and missed the chance to move above Rangers into second place in the Clydesdale Bank Premier League.
They now find themselves too far behind Celtic to deprive the leaders of a title party should Neil Lennon's men win at Ibrox on Sunday.