The 2013–14 season was a breakthrough year for Urech and teammates Binia Feltscher, Irene Schori and Franziska Kaufmann. At the start of the season, the won the 2013 Red Deer Curling Classic and made the playoffs of the Stockholm Ladies Cup and the Women's Masters Basel. They also won the right to represent Switzerland at the 2014 World Women's Curling Championship in Saint John, New Brunswick, Urech's first World Championship. They had a great round robin, finishing in second with a 9–2 record, only losing to South Korea and Russia. This sent them to the 1 vs 2 game against Canada's Rachel Homan which they would lose 8–3. Switzerland quickly rebounded in the semifinal against Korea's Kim Ji-sun setting up a rematch against Homan. After a slow first half, the Swiss team would score three points in the eighth end and steal three in the ninth, giving them a 9–5 lead going into the final end. They successfully ran the Canadians out of stones to secure Switzerland's fourth World Championship title.