Davies, younger brother of Wales and British and Irish Lions centre Jonathan, is among 10 changes made by head coach Warren Gatland following a 37-27 defeat against Ireland 11 days ago.
And fit-again Bath number eight Faletau skippers a team that also sees wing George North, centre Owen Watkin, fly-half Gareth Anscombe and hooker Elliot Dee handed starts.
The five starting XV survivors from Dublin are Liam Williams, who moves from wing to full-back instead of Leigh Halfpenny, wing Steff Evans, centre Hadleigh Parkes, scrum-half Gareth Davies and lock Cory Hill.
Regular skipper Alun Wyn Jones is rested, while Gatland has opted for a new-look back-row of Davies, Justin Tipuric in the number six shirt and Faletau, who makes a first appearance in this season’s tournament and captains his country for the first time.
Davies, 27, was an integral part of the Scarlets’ PRO12 title triumph last term, in addition to helping them reach this season’s European Champions Cup quarter-finals. He also featured for GB’s Olympic silver medal-winning rugby sevens squad at Rio 2016.
North’s selection comes four days after missing his club Northampton’s Aviva Premiership game against Sale Sharks, after which interim Saints boss Alan Gaffney suggested the 25-year-old had not wanted to play for Saints.
North had been released by Wales as it was a Six Nations fallow week, but he did not feature for Northampton amid reports he had an arrangement with former Saints rugby director Jim Mallinder that he would not play club rugby on rest weekends.
Wales will be desperate to hit back following successive losses at Twickenham and the Aviva Stadium, but Gatland has still made more changes than many might have expected.
Gatland said: “It is a great opportunity for Taulupe. He is a world-class player, hugely experienced and this will be great for his development and we are looking forward to seeing those leadership qualities come through.
“We have made some changes, but we are bringing in a lot of quality and a lot of experience with the likes of Bradley Davies, Justin Tipuric, George North and Taulupe.
“Add into that James Davies, who gets his first cap, and Elliot Dee, who gets his first start – this is a great opportunity for them to play tournament rugby.
“It is challenging making changes, but we have picked a really exciting team, and Sunday is their chance.”
The replacements’ bench includes Wales’ entire first-choice front-row of Rob Evans, Ken Owens and Samson Lee, while there are also chances for highly-rated Cardiff Blues forwards Seb Davies and Ellis Jenkins.
Wales: 15 Liam Williams, 14 Steff Evans, 13 Owen Watkin, 12 Hadleigh Parkes, 11 George North, 10 Gareth Anscombe, 9 Gareth Davies, 1 Nicky Smith, 2 Elliot Dee, 3 Tomas Francis, 4 Bradley Davies, 5 Cory Hill, 6 Justin Tipuric, 7 James Davies, 8 Taulupe Faletau (c)
Replacements: 16 Ken Owens, 17 Rob Evans, 18 Samson Lee, 19 Seb Davies, 20 Ellis Jenkins, 21 Aled Davies, 22 Rhys Patchell, 23 Leigh Halfpenny.