Costelow and Leicester wing Hamer-Webb were two of four changes to the starting side announced by coach Steve Tandy on Thursday following last week's 54-12 thrashing by France - Wales' 13th straight Six Nations defeat.
Costelow, in for Dan Edwards, and Hamer, who replaces Ellis Mee, are the only two changes in the back division.
Scarlets stand-off Costelow has not played for Wales since a defeat by Japan at Kitakyushu last July.
In the pack, Taine Plumtree takes over at blindside flanker and Ben Carter is selected ahead of Adam Beard at lock.
Beard was heavily criticised after his miscued kick led to France's fourth try in Cardiff last weekend.
Plumtree comes into a reshaped back row with Olly Cracknell dropping out and veteran Aaron Wainwright moving to No. 8.
Bath-born Hamer-Webb, who represented England Under-20s in the Six Nations, has made eight appearances for Leicester since moving from Cardiff last summer.
The 25-year-old qualifies for Wales through his Cardiff-born mother.
Wales (15-1)
Louis Rees-Zammit; Gabriel Hamer-Webb, Eddie James, Joe Hawkins, Josh Adams; Sam Costelow, Tomos Williams; Aaron Wainwright, Alex Mann, Taine Plumtree; Ben Carter, Dafydd Jenkins; Tomas Francis, Dewi Lake (capt), Rhys Carre
Replacements: Ryan Elias, Nicky Smith, Archie Griffin, Freddie Thomas, James Botham, Kieran Hardy, Jarrod Evans, Blair Murray
Coach: Steve Tandy
