Cartwright's side scored all their points in the first half on Thursday as they ran in tries through Cade Cust, Herman Ese'ese, Lewis Martin and Sam Eseh while an inspirational Aidan Sezer kicked five goals in his 250th career appearance.
The Australian coach said: "We set it up in the first half. The first 15 minutes was an arm wrestle but we didn't panic and stuck at it.
"We then got a bit of decent ball and Sezer was at his very best on his 250th.
"To go out and compete like they did, and attack the way they did, it was good to see.
"I know we're capable of that. It's not always possible to do every time we go out and play but tonight was nice and clinical."
Leigh coach Adrian Lam held the opposite view of his side and was heavily critical of the Leopards' defence.
Lam said: "I'm very disappointed. I didn't see that coming.
"They were 10 times better than us but when you make decisions like we made, it can really hurt you heavily.
"There were several players that played their worst rugby of the year. It was unacceptable."
Tries from Edwin Ipape and Owen Trout in the final quarter added some respectability to the scoreline but the result was never in doubt.
Ex-NRL star Sezer was at his creative best for Hull, spreading the play for Cust to show his strength to burrow through several challenges to touch down.
Sezer then landed a 40-20 kick which led to Will Pryce driving close to the line and Ese'ese crashing over.
Another followed on the stroke of half-time, Eseh finishing off more good work from Sezer under the posts. With five goals from Sezer, Hull held a commanding 26-0 advantage at the break.
Ipape finally got them on the scoreboard with just over an hour gone when he wriggled under the posts after a Tesi Niu break and Ben McNamara converted.
Trout cut the arrears further and Josh Charnley threatened to create another after an electric break, but Sezer got back to cut out Ipape's pass.
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