And they had their new-look strike duo of Jamie Mole and Mauricio Pinilla to thank principally for the points.
For the pair, playing together for the first time, gave the Inverness defence a torrid afternoon and helped themselves to a goal apiece.
With Neil McCann causing problems down the left, Caley went behind when the winger's low cross was volleyed home by Pinilla after 19 minutes.
But shocking defending from debutant Jose Tiago allowed Caley an equaliser after half-an-hour when Graham Bayne ran across the Portuguese full-back to nod home Barry Wilson's cross.
And the Highlanders might have gone ahead with Wilson's angled drive deflected into the side netting and Dennis Wyness heading narrowly wide.
But these missed chances proved costly when Hearts regained the lead three minutes from half time. Hartley's free-kick from the right was met powerfully by Mole, whose header flew in off the underside of the bar.
In the second half, Mole's cross fell for McCann and his blistering volley crashed off the bar, but substitute Andrew Driver made no mistake when he capitalised on Ross Tokely's poor clearance to thunder home a close-range volley.
And fellow substitute Bruno Aguiar rounded off the scoring when he prodded home Mole's header two minutes from time.