London Wasps full-back David Doherty, Sale centre Andrew Vilk and Harlequins full-back Tom Williams completed the scoring for Ben Ryan's side, who are going in search of an unprecedented fifth consecutive title in Hong Kong this weekend.
Williams, who spent the majority of his childhood in Hong Kong, opened the scoring with a solo burst from halfway before Amor crossed to extend the lead to 14-0 lead after two and a half minutes.
But the hosts, backed by the passionate home crowd, responded and after a sustained period of pressure inside England territory Ricky Cheuk crossed in the corner to reduce the deficit to 14-7.
England regained the 14-point cushion just before the break as 22-year-old Vilk crossed for his maiden Sevens try after quick work by Amor around the halfway line allowed the Sale centre to burst clear of the Hong Kong defence and score in front of the South Stand.
England maintained their dominance in the second half and Care opened his account just after the restart before grabbing a second to open up a 33-7 advantage.
Doherty completed the scoring with just over a minute remaining with a try in the corner.
"Hong Kong are a good side, very physical, and very competitive at the break down," said Amor.
"The first game is always a tough one, it doesn't matter who you are playing, we did well to come out on top. The score flattered us as it's a very good Hong Kong side.
"We've still got a long way to go, but we've got the potential to be very good by the end of the tournament."
England complete their games in Group E against Korea and Argentina on Saturday.
Fiji, winners at the last tournament in San Diego, ran in seven tries during a 45-0 victory over minnows Sri Lanka in the opening game of the tournament in Group A, while South Africa were equally impressive in beating Chinese Taipei 59-0 in Group B.
China produced a valiant effort in losing 49-5 to powerhouse Samoa in Group C, while the USA edged out France 15-5 in Group F.
New Zealand, who top the Sevens series table after four events alongside Fiji, ran in seven tries during a 41-5 demolition of Italy.