Alosio Yamo Yamo put the Americans 7-0 up after running in right under the posts and New York extended their lead through Derek Lipscomb.
Gareth Stoppani added a third try on the stroke of half time and New York continued to dominate with Jon Kokinda touching down to kick off the second half.
Steph Reynolds pulled one back for the Cherry and Whites but Augspurger finished the job for his side and said he believes the Americans were spurred on by their underdog tag.
"It feels great to lift the trophy. I don't think anyone expected us to be in the cup quarters let alone take home some hardware," he said
"All of us had to believe that we were going to be there. When you are considered the underdog it kind of drives the team to play better.
"We showed that rugby is getting better in the US and a lot of people are curious about how USA Rugby is doing.
"We know how to play and so I'm extremely proud of both San Francisco and our team."
New York claimed their place in the plate after a 26-19 win over VVA Saracens Moscow region.
They went ahead through Yamo Yamo but Aleksandr Ianiushkin hit back with an unconverted try.
Chris Rose put the Americans ahead again before Ilya Babev leveled things but tries from Liscombe and Augspurger sealed victory.
Gloucester advanced after an end-to-end match against San Francisco ended with the Cherry and Whites on top by 26-14.
Rhodri McAtee opened the scoring for Gloucester but Jack Halalio drew the Americans level.
Reynolds and McAtee put Gloucester in control and, despite a dazzling Carlin Isles try, Dan Robson touched down late on to put the game beyond doubt.
And Dmitry Perov and Babev both scored twice as Moscow beat San Francisco in the 7th/8th place playoff by 33-12.
Nikolay Goroshilov and Igor Klychnikov added scores for the Russians while Isles side-stepped three tackles to pull one back and Neil Barrett grabbed a consolation for the Americans.
PLATE SEMI RESULTS
New York 26 - 19 VVA Saracens Moscow Region
Gloucester 26 - 14 San Francisco
7th/8th PLAYOFF RESULT
San Francisco 12 - 33 VVA Saracens Moscow Region
PLATE FINAL RESULT
New York 33 - 14 Gloucester