Van Egmond was unable to contain his anger after a tense first half as the Newcastle boss argued strongly with match officials and followed them down the players' race to continue the discussion.
And the Jets' star import Emile Heskey capped an unhappy game by arguing with the referee after fulltime.
Heart scored just its fourth win of the season to go to 15 points, two ahead of Sydney FC, while the Jets remain on 16 points after suffering their eighth defeat in 14 matches.
Coach John Aloisi's men held a 2-1 advantage at halftime and were able to defend their lead in a scoreless second half in front of 5641 fans.
Golgol Mebrahtu put Heart 1-0 up in the sixth minute with a powerful right-foot strike after linking up with Josip Tadic.
A clever pass from former England international Heskey set up a goal-scoring opportunity for Ryan Griffiths, who was ankle-tapped by Heart goalkeeper Andrew Redmayne in the 18th minute which earned a yellow card.
Griffiths scored with the resulting penalty to level the scores at 1-1 but, eight minutes later, Heart was back in front after another penalty as Redmayne's rival goalkeeper Mark Birighitti was yellow-carded for lunging at the feet of Jonathan Germano.
Tadic scored with the penalty attempt to put Heart ahead 2-1.
Newcastle's Craig Goodwin was yellow-carded for an ugly challenge on the wing in the 44th minute.
Goodwin almost produced a sensational goal just before halftime with a long-range strike that was tipped over the top by Redmayne, a 23-year-old in his starting debut for Heart.
A Heskey header on goal was well saved by Redmayne in the 48th minute in a lively start to the second half.
Heskey produced another dangerous header in the 79th minute which was saved on the line by Redmayne.
The former Liverpool star's frustrations spilled over in the 86th minute when Heskey was yellow-carded for dissent.
British-born Heskey, whose father came from the Caribbean island of Antigua, arranged for Antigua and West Indies cricketing great Viv Richards to address the Jets players before the game.
Richards, who attended the match, is spending the Australian summer in Melbourne as a mentor for Big Bash League Twenty20 cricket team the Melbourne Stars.