Warren Gatland's Welsh team are seeking to avoid a 10th successive Test defeat after a horror run, with Australia showing more than a passing interest in the outcome of Sunday's match as they play Wales next, after their England opener, on the 'grand slam' tour.
The 24-year-old Murray qualifies for Wales through his mother and has only recently signed for the Scarlets, but gets an immediate chance to impress.
"I think he's been playing well for the Scarlets," coach Warren Gatland told reporters on Friday. "He hasn't had a lot of games. He came through the New Zealand pathway. We were pretty excited when he committed to us. He gives us a left-footed option which we haven't had in a while. He gets touches and defends well."
Gatland has also selected several less experienced players, including centre Max Llewellyn, who has two previous appearances, his midfield partner Ben Thomas (four caps) and prop Archie Griffin (three).
"We have excellent competition in the squad, so it was a tough selection and there were some close calls but I think there's a really nice balance for Sunday. We have some experienced players back alongside some exciting youngsters," Gatland said.
Anscombe, making a first Wales appearance since last year's Rugby World Cup when his 23 points with the boot helped crush Australia, has been preferred to Sam Costelow, who is among the replacements, and will have the vastly experienced Tomos Williams alongside him at halfback.
Fiji, who also beat Australia 22-15 in France last year, have made four changes and one positional switch to their backline as they welcome back several experienced players.
Vuate Karawalevu moves from the wing to fullback, with Jiuta Wainiqolo taking his place in the number 14 jersey.
Waisea Nayacalevu and Josua Tuisova take over as the centre-pairing, with Semi Radradra also into the team on the opposite wing.
The changes will boost a side that was thumped 57-17 by Scotland last weekend in a game that fell outside of the international window.
Fiji's only previous victory over Wales in 14 Tests came at the 2007 World Cup in France, though they did also manage a draw in 2010.
Wales
15 Cameron Winnett, 14 Mason Grady, 13 Max Llewellyn, 12 Ben Thomas, 11 Blair Murray, 10 Gareth Anscombe, 9 Tomos Williams, 8 Aaron Wainwright, 7 Tommy Reffell, 6 Taine Plumtree, 5 Adam Beard, 4 Will Rowlands, 3 Archie Griffin, 2 Dewi Lake (captain), 1 Gareth Thomas.
Replacements: 16 Ryan Elias, 17 Nicky Smith, 18 Keiron Assiratti, 19 Christ Tshiunza, 20 James Botham, 21 Jac Morgan, 22 Ellis Bevan, 23 Sam Costelow.
Fiji
15 Vuate Karawalevu, 14 Jiuta Wainiqolo, 13 Waisea Nayacalevu (captain), 12 Josua Tuisova, 11 Semi Radradra, 10 Caleb Muntz, 9 Frank Lomani, 8 Elia Canakaivata, 7 Kitione Salawa, 6 Meli Derenalagi, 5 Temo Mayanavanua, 4 Isoa Nasilasila, 3 Samuela Tawake, 2 Tevita Ikanivere, 1 Eroni Mawi.
Replacements: 16 Sam Matavesi, 17 Haereiti Hetet, 18 Jone Koroiduadua, 19 Mesake Vocevoce, 20 Albert Tuisue, 21 Simi Kuruvoli, 22 Isaiah Ravula, 23 Sireli Maqala.
