The Tynecastle side's defending in the first period was truly calamitous, summed up by a failure to keep out Mika Baur's effort just before half-time. The German showed lovely skill and composure to waltz through before Stephen Kingsley's attempted goalline clearance rebounded off Jamie McCart and rolled apologetically in.
Celtic's fifth and referee David Dickinson had yet to blow for the interval.
Laurent Mendy's fine, curling effort had briefly reduced Hearts' deficit to three but, given Reus's heroics to keep out Nygren, added to the fact Haissem Hassan had smacked a lovely shot off the keeper's right-hand post, a four-goal advantage at the break didn't flatter Celtic at all.
It became five within four minutes of the restart when Camilo Duran gave a flowing move the first-time finish it deserved. And Nygren slammed in a seventh late on to complete the rout.
This was total domination from Celtic against a strangely hapless Hearts, who didn't really make their hosts work particularly hard for the majority of the riches they gleefully plundered.
A statement win for O'Neill's league leaders. A sobering defeat for new Hearts boss Wouter Vrancken, who's likely to remember his first visit to Celtic Park as much as he'll be desperate to forget it.