England, who were in only their second final in the New Zealand capital, were trailing 17-5 at half-time but fought their way back with tries to Robert Vickerman and one at the death by Isoa Damudamu to deny New Zealand their fifth crown on home soil.
The win leaves England and New Zealand tied on 44 points in the IRB Sevens Series standings, just four points behind South Africa who won the Plate competition.
It was England's first tournament win since Hong Kong in 2006 and the first for coach Benjamin Ryan.
Favourites coast on day one in HK
The South Africans defeated Wales 26-12 in the Plate final to ease the heartache of their Cup quarter-final loss to New Zealand earlier in the day.
Scotland also captured their first piece of silverware this year, defeating minnows Niue to win the Shield.
England got off to the worst possible start in the final, conceding a try to Paul Grant then another to Zar Lawrence after a chance went begging at the other end.
They were soon 15-0 down when Oliver Phillips was robbed of the ball close to his own line by DJ Forbes who burrowed his way over.
Phillips made amends just before half-time though, when he held off speedster Viliame Waqaseduadua to go over in the corner.
It sparked a turnaround in fortunes, as Vickerman intercepted a speculative pass by Lote Raikabula close to his own line to run in under the posts and give Gollings a simple conversion.
Vickerman and Tomasi Cama were then sin binned for an exchange of blows before Damudamu struck to hand Gollings his match-winning kick.
England Coach Ben Ryan said, "It's amazing. The final whistle went and Damu was galloping over the tryline.
"This is my first tournament win and this is England's first tournament win in New Zealand. We're one tournament away from the World Cup so this is good timing for us.
"We have worked really hard to get to this point. We've had consistency in our players, they're fit and they have a lot of belief.
"We were well beaten by Argentina yesterday. Today we gathered our thoughts and played three outstanding games of rugby and I'm delighted for them, they deserve it.
"Our job is to develop these players. Playing away from home against a New Zealand side who have huge support is testing but the boys played to their potential. If we can win here then we have a pretty good chance everywhere else we play."
Earlier in the day, England had to come from two tries down to defeat Fiji 31-10 in a gripping Cup quarter-final.
That earned them a semi-final against Kenya, who they easily accounted for with Phillips scoring a hat-trick in the 26-0 victory.
Wales' hopes of a rare Cup semi-final appearance were quashed by Kenya, who won their quarter-final 10-7.
Tries to Collins Injera and Humphrey Kayange put them 10-0 up and, although Wales clawed back one through Aled Thomas, who converted, they could not find the match-winning score they needed.
But having claimed the prized scalp of New Zealand on day one, Wales added Fiji to the list with a 14-12 plate semi-final win.
Scotland won the Shield after overcoming the disappointment of losing 22-12 to Australia in their Bowl quarter-final.
They then accounted for Canada 14-7 in the Shield semi-finals before scoring four tries in their 26-0 win against Niue.
The Cook Islands beat Tonga 24-10 to win the Bowl final.
Rugby waits for Olympic inclusion
England off to flyer in Hong Kong