Victorian Nathan Holman was narrowly beaten in the afternoon Round of 16 match against the co-medalist on Tuesday, England's Neil Raymond, his brave bid coming to an end.
For Goss it will be the second year in succession he has reached the quarter finals of the game's most significant amateur event.
Watt, the co-medalist in qualifying on Tuesday, defeated Atlanta's Seth Reeves in his morning round, going one up at the first and making the turn four ahead before winning comfortably 3 & 2.
In his afternoon matchup against Canadian Charlie Hughes, Watt fought back from an early deficit before drawing clear to win 2&1.
Goss never trailed in his morning match against Missouri's Carr Vernon although it was a very tight battle, the 19 year old finally winning two up at the last.
Goss's afternoon opponent, Californian Xander Schaufelle, appeared more than a handful early and through eight holes held a one hole lead. Goss, however, drew clear with a brilliant stretch over the closing few holes including an eagle two at the par four 17th to win 2&1.
In tomorrow's Quarter Final Watt will play Pennsylvania's Brandon Matthews while Watt tackles Texan Scottie Scheffler.
Unfortunately for Australian golf if both are to win their matches tomorrow, Goss will play Watt in one Semi Final so only one can now make the 36 hole Final.
Let's hope there is such a problem as it will mean there is at least one Australian into the final.
The last time the pair met in such intense competition was when Goss defeated Watt in a playoff for the PGA Tour of Australia's West Australian Open at Royal Perth last October.
There is still a lot of golf to play before then but either way both have done very well to date as had Nathan Holman.
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