Four first-half tries put the Warriors well on their way to a solid win on home soil and, despite their opponents pulling one back on the hour, it was plain sailing into the final four of the competition.
It did not take too much longer for Wigan to bag themselves a second to create some breathing space, as Tomkins this time darted past Grant Millington and touched down under the posts.
Warriors had a seemingly unassailable lead before the interval thanks to Charnley, who bagged his second and the hosts' fourth score of the night with a dive over the chalk right in the corner.
A glimmer of hope was provided for Cas - who had won their last three cup ties here stretching back to 1948 - when Luke Gale finished off a well-worked move under the posts, before converting from the follow-up kick to drag his side within 16 points of their opponents.
The momentum that the Tigers so much craved did not follow, though, and Dom Manfredi controversially crossed over in the final quarter of the match to seal things for Wigan, making Ben Crooks's late try a mere consolation.
Wakefield Trinity Wildcats, Warrington Wolves and Hull FC join the Warriors in the final four of the competition.