Van Barneveld, seeded 14th for the tournament, made short work of his opening match against the 20-year-old Austrian with three dominant set wins.
The 2007 winner, and five-time world champion, checked out the two highest finishes of the tournament so far - 167 and 170 - on his way into the last 32.
Jamie Caven overcame problems with his doubles to book his placed in the second round with a 3-2 win over Jason Hogg.
The 19th seed only hit 11 of his 46 attempts at doubles in the match, but his high scoring gave him enough breathing space to hold of Hogg's challenge.
"I was made to sweat there for that," he said.
"I never played at my best at all, the doubles were a problem, but I've played better than that and lost so you just have to take the win, and come back stronger."
Michael's Smith's victory over Mensur Suljovic was a little easier, the number 22 seed beating the 42-year-old 3-1 having been a set behind.
Smith hit nine 180s in the match and finished with an 97.47 average as he moved onto the next round, securing the win in style by taking 76 on the bullseye.
Meanwhile, qualifier Nolan Arendse set up a match with Brendan Dolan after beating Alex Hon 4-0 in the preliminary round.
Later, Northern Ireland's 11th seed Dolan dished out a rout of his own winning nine legs without reply to beat the South African Arendse 3-0.