Chester conceded 40 unanswered points in the second half as their more experienced opponents ran out 60-4 winners on a miserable day for the Gladiators.
Newton opened the scoring after seven minutes and ran in two more tries to take a 14-0 lead as the hosts dominated the early proceedings.
Chester began to work their way back into the game and Damon Williams scored in the corner on 19 minutes to get them off the mark, but that was as good as things got for the Gladiators.
Storm added another try on 36 minutes to take a 20-4 lead into the break before Chester's second half collapse.
Newton took advantage of some slack Gladiators defence to score eight tries in the second period as Chester struggled to make any headway and were unable to cope with Storm's powerful forwards.
Youngster Joe Hughes and Mike Walker stood up well, producing some excellent tackles, while 16-year-old Ed Wilkinson had a solid debut.
Paul Foster was named at the Bartletts Solicitors Man of the Match for the Gladiators.
Chester will be looking to bounce back to winning ways when they host Widnes West Bank at Sealand Road next week.