Headers from Shinnie and then Holt had Neil Lennon’s players comfortably ahead at the interval with Cummings and Graham adding two more in the second half to make it four straight league wins for Hibs.
Israeli goalkeeper Ofir Marciano made an immediate debut for Hibs after finally getting clearance to play in Scotland, while Shinnie began a match in a green and white shirt for the first time as Ross Laidlaw and James Keatings dropping to the bench.
But there was no Dylan McGeouch, out with a minor knock, for Lennon’s side as Fraser Fyvie made his first start of the season following a knee problem.
The Hibs players wore black armbands to mark the death earlier this week of the club’s oldest fan, Sam Martinez, who passed away at the age of 106.
Hibs started brightly and Morton defender Jamie Lindsay came to his side’s rescue after just seven minutes when he was in the right place to clear Holt’s shot after the striker had peeled off his marker to meet John McGinn’s corner.
It took a terrific save from Derek Gaston to deny Shinnie as he met Cummings’ cutback. The Morton goalkeeper got down low at his right hand post to push the ball aside.
There was nothing Gaston could do, however, to prevent Hibs going ahead in the 29th minute. Fyvie’s deep cross from the right eluded everyone except Shinnie at the back post and the midfielder nodded the ball down into the net.
Hibs might have doubled their lead six minutes later, Shinnie and Holt combining to give Cummings a run in on Gaston but the leading scorer could do no better than stab a low shot inches wide.
Hibs increased their lead four minutes before the interval. McGinn threw in an inviting cross from the left which Gaston probably thought was his - but he was reckoning without Holt who rose above the Morton keeper to power home a terrific header.
Morton looked beaten at half-time and they found themselves three down nine minutes into the second period, David Gray feeding the ball down the line for Shinnie to clip in a cross which Cummings nodded home from inside the six yard box.
There had been little to trouble Hibs but McGinn surrendered possession on his own bye-line, allowing Lindsay to fire in a low cross - happily for the Capital side they had sufficient numbers back to avert the danger.
Morton were forced to replace Gaston with former Hibs goalkeeper Andy McNeil and it wasn’t long before he was picking the ball out of his net - not that he could do anything about it.
He was left helpless as Brian Graham, who had replaced Holt, threw himself at a superb Cummings cross, directing a terrific header into the bottom corner of the net.
Martin Boyle had a great chance to make it five but shot straight at McNeil when left with only the goalkeeper to beat
Hibs: Marciano, Gray, McGregor, Hanlon, Stevenson, Bartley (Keatings 69), Fyvie, McGinn, Shinnie, Cummings (Boyle 78), Holt (Graham 64).
Substitutes not used: Laidlaw, Forster, Harris, Crane.
orton: Gaston (McNeil 71), Doyle, Kilday, O’Ware, Russell, Lindsay, Forbes, Tidser, Nesbitt, Oliver (McAleer 82), Quitongo (Oyenuga 64).
Substitutes not used: Scullion, McDonagh, Tennent, Tiffoney.