Welsh's win came after America's Tara Kirk saw off Australian competition to win the 100m breaststroke, striking a blow for the resurgent US team.
The world record-holder timed a championship best 1:05.25 sec to finish ahead of South African Suzaan Van Biljon and Australia's Jade Edmistone, who won the 50m event on Thursday.
Brooke Hanson, who took a record-equalling six titles for Australia at the last Short-Course Championships two years ago, was fifth.
Australia moved on to eight gold medals, ahead of the United States on five, with three more events to be decided on the penultimate night.
Results (Finals):
Men:
50m backstroke: 1. Matthew Welsh (AUS) 23.53; 2. Thomas Rupprath (GER) 23.70; 3. Helge Meeuw (GER) 24.01
50m butterfly: 1. Matthew Welsh (AUS) 23.05; 2. Sergiy Breus (UKR) 23.06; 3. Kaio Almeida (BRA) 23.07
Women:
100m breaststroke: 1. Tara Kirk (USA) 1:05.25 (championship record); 2. Suzaan Van Biljon (RSA) 1:05.62; 3. Jade Edmistone (AUS) 1:06.08. —AFP