I recall a thread about this some time back. The 7-0 game was definitely a landmark moment when it came to changing Hearts' mindset towards the derby. Gary Mackay and Dave Bowman (who were both young Hearts fans at the time) have both spoken about how they grew up in an era when Hibs seemed to beat Hearts pretty much every time they played them and that when Hearts finally came back up to the top flight in 1983 it definitely inspired them to change the yam mentality around the fixture.
In saying that, Hibs should have won the first game between the sides for four years. We were 1-0, then 2-1 up and in control at Tynecastle but let things slip and a young John Robertson scored at least one of the Hearts goals in a 3-2 win. In the next derby at ER we were also ahead (through Bobby Thomson IIRC) and looking comfortable before a speculative shot by Robbo took a massive deflection and got them a draw*. Those games set the tone for the fixture for a long time after that.
*Here's that deflection (which Archie McPherson somehow initially fails to spot):
https://www.youtube.com/watch?v=kHArA4C1PfM