While there can be no doubt Aberdeen were aided by that Hanley red card and the resultant Nisbet penalty, the hosts had started brightly before that.
Over the course of the first 45 minutes, Stephen Robinson's side had nine shots, generated an xG (expected goals) of 1.63 and enjoyed over 50% possession, while they played 225 passes compared to Hibs' 194.
They looked like a team that finally had a bit of confidence and probably should have been more than one goal to the good.
Olusanya was deemed offside when he turned in Lyall Cameron's cross. Alexander Jensen skied an effort from six yards out. Stuart Armstrong fired wide. And Nisbet had a header saved by Sallinger.
Aberdeen's dominance continued into the second half, with more than half the possession and a further eight shots, six of which were on target. That was rewarded with Nisbet's second which made for an ultimately comfortable afternoon.
That victory moved Aberdeen up to eighth - level on points with Dundee but ahead on goal difference - but crucially three points above St Mirren in 10th and five clear of Kilmarnock in relegation play-off place.
For Hibs, the tests only get tougher as they head into the split and it will be crucial to show a reaction if they want to keep their push for European football alive.
The good news for David Gray's side is that Motherwell were also beaten, keeping the gap between them at three points.
Hibs will also be keeping a close eye on Falkirk's home game against Rangers on Sunday because if John McGlynn's side win, they'll be just two points behind Hibs with five games to go.