Irankunda's finish was superb, a brilliant touch inside after collecting a pass from Paul Okon-Engstler giving him space to find the low strike.
Turkey, appearing in the World Cup for the first time since 2002, were dominant for large parts but could not find an equaliser at BC Place.
Defender Abdulkerim Bardakci tried a speculative effort from distance and it took a fine save from Australia goalkeeper Patrick Beach to tip it on to a post.
Beach, a surprise starter ahead of Mat Ryan as he made his first competitive international appearance, also denied Arda Guler from a free-kick and a close-range effort from Zeki Celik in the second half.
Midfielder Metcalfe pounced on some sloppy play from Turkey before firing a low strike into the bottom corner.
Australia will play hosts USA in Seattle on Friday at 20:00 BST, while Turkey take on Paraguay in San Francisco on Saturday at 04:00 BST.