Three first half goals put the Gers in control the break before two second half goals from substitutes Ure and Graham rounded off a dominant performance for the hosts.
Speaking to RangersTV after the victory the head coach praised his team for their strong performance against the Championship side: "I am naturally pleased, I thought it was a strong performance, I thought we maybe started a little bit slow, but I think as the game panned out in the first half the more we played closer together.
"We caused them problems and created opportunities, obviously it has taken Tony’s special goal in terms of the way he has finished it from off the angle of the box into the far corner to get us on our way.
‘’But I think over the course of the game we showed a lot of control and created a lot of good opportunities’’.
There were five different goal scorers for the Light Blues in a five-star display and the manager was happy with the variation and seeing the goals shared around.
"If you look at Zak’s goal, it is a nice goal which Johnly sets into his path, there is combination play that allows Charlie to get in for his goal.
"Then you look at the second half and the impact of the subs as well, Robbie Ure’s is a great goal from an excellent pass from Connor Young.
"James Graham seems to be scoring these types of goals at the moment coming off the side of the box and passing the ball into the corner, so it was a good variation and spread of the goals as well."
McCallum’s side are the defending champions in the cup competition, and he says he has challenged his team to try repeat the feat and retain the trophy again.
"We spoke before the game this is a different one now, there is different competitions that we have played in this season, today was the restart of the Glasgow Cup it has been a while since we have played in it.
"Today the challenge was to start properly, to start on the front foot and get a good result, and to challenge ourselves to achieve what we did last season, but first and foremost it is dealing with the individual games.
"We enjoyed the fact that Partick Thistle brought a mixture of first team and young players, that allows our young guys to go and play against some senior pros as well and it is a good experience for them.
"That is also one of the reasons why we enjoy this competition because the challenge is different from playing against players of a like for like age.
"You are playing against a Championship team and play at that level so it important that we get that challenge and the lads have enjoyed that."
Hear from Bailey Rice and David McCallum after today's victory.