Tom Johnstone scored twice in the second period following first-half scores from Toby King and debutant Mikey Lewis.
Tonga showed they will be no pushovers as the first Pacific island nation to tour England, leading early on through Starford Toa and Tyson Frizell.
Tolutau Koula added a late score for a grandstand finish, but England held on.
The series continues in Huddersfield on 28 October, before concluding in Leeds the following weekend.