Jets coach Gary van Egmond paired Heskey and Michael Bridges for the first time this season, starting the former Premier League players in behind Socceroo Adam Taggart and the tactical change paid off as Newcastle looked much more dangerous in front of goal as they outplayed the Heart for the majority of the contest.
Heskey opened the scoring in the 10th minute with a wonderful strike before Griffiths sealed the win with a smart goal 10 minutes from the final whistle.
Heart striker Eli Babalj threatened every time he got the ball, rattling the post in the 25th minute but for the most part, the visitors were forced to attack on the counter.
The Jets dictated play from the outset and went ahead courtesy of a thundering effort from Heskey.
Griffiths played an intelligent ball into the box for the former England international who slammed a right-foot strike from 15 metres out that squeezed under Heart goalkeeper Andrew Redmayne and into the net.
And the hosts made sure of the points late on when Taggart played in Griffiths who streaked into the box before lobbing a shot over Redmayne for his ninth goal of the season.