Kenya had led 19-12 but after they loss two players to the sin bin England were able to score two late tries through Christian Lewis-Pratt, to take the match to Extra Time, and then Sam Edgerley to win it.
Having trailed 14-0, Mike Friday's side scored two second-half tries to take the match into sudden death extra time before Oscar Ouma scored the all-important try, his second of the match.
New Zealand still finished third overall, beating Samoa 17-7 in the third place play-off.
Ben Ryan's side booked their place in the final beating Samoa 21-19. Trailing 12-0, Christian Lewis-Pratt (twice) and Marcus Watson gave them a 21-12 lead which proved enough despite Lio Lolo's effort.