Greig, a former inline skater who only stepped onto the ice for the first time five years ago, was second in the 500m in 35.17 seconds, just 0.05 behind his best mate and training partner Michel Mulder of the Netherlands.
"We are super excited with this result," coach Desly Hill said. "Daniel was the best he has been in his short skating career so far. He had personal records for the openings and also for sea level races."
The 22-year-old skater, not only grabbed the silver medal for his efforts and set personal records, but impressed everyone by being the only athlete to improve on his 500m time from the previous day.
But the accolades didn't end there for the young Victorian skater.
A couple of hours later, Greig went on to finish a credible fifth in the 1000m.
Greig drew the inside lane against Dutch skater Ronald Mulder, the twin brother of Michel who won last night's 500m event.
The pair were evenly matched throughout the 1000m race, with Greig snatching the win by just 0.24 seconds to finish in 1:10.35.
The 22-year-old Victorian was just 1.39 seconds off the pace of eventual winner, Shani Davis of the United States. Davis, the defending Olympic Champion over 1000m from the past two Olympic Games, took out the title in 1:08.96.
Denis Kuzin of Kazakhstan and Michel Mulder of the Netherlands rounded out the medals.
Greig's two silver medals and fifth place meant that he finished third overall at the World Championships behind Michel Mulder and Davis.
He will now head back home for final training and preparation ahead of the Sochi 2014 Games which get underway on 7 February.