Flyhalf George Ford will captain the side in the first of England's World Cup warm-up matches.
Heinz now has a chance to force his way into England's World Cup squad in a match that takes place just a day before coach Eddie Jones names his 31-man party for Japan 2019.
Ben Youngs, England's first-choice scrumhalf, is on the bench.
Bath wing Ruaridh McConnochie is also set to win his first cap after impressing in the English Premiership last season.
Meanwhile left wing Anthony Watson will be making his first appearance for England since damaging his Achilles at the end of the 2018 Six Nations.
There is no place in the matchday 23 for regular captain and flyhalf Owen Farrell, while Piers Francis gains from Ben Te'o's absence from the training squad by winning his fourth cap alongside Henry Slade in the centres.
Sam Underhill and Tom Curry start in the same back row despite being specialist opensides with Curry packing down at blindside flanker.
The first of two back-to-back matches against Wales sees prop Dan Cole and locks Joe Launchbury and Charlie Ewels all selected.
Jones, brought in after England's first-round exit at a a 2015 World Cup on home soil, said dethroning reigning champions New Zealand remained his sole target.
"We have completed our four weeks of pre-season training and now we have moved into four weeks of warm up games ahead of the Rugby World Cup," Jones said after naming his side.
"Our focus has now changed to match preparation and fitness and creating a game that will stand up to the rigours of the tournament where we have to win seven games in seven weeks.
"Our team selection and tactics in our next four games are all about developing a team capable of winning in Japan and our overarching target of being ready when we get on the plane on September 8 to win the World Cup."
15 Elliot Daly; 14 Ruaridh McConnochie, 13 Henry Slade, 12 Piers Francis, 11 Anthony Watson; 10 George Ford (captain), 9 Willi Heinz; 8 Billy Vunipola, 7 Sam Underhil, 6 Tom Curry; 5 Charlie Ewels, 4 Joe Launchbury; 3 Dan Cole, 2 Luke Cowan-Dickie, 1 Ellis Genge
Substitutes: 16 Jack Singleton, 17 Joe Marler, 18Harry Williams, 19 George Kruis, 20 Lewis Ludlam, 21 Ben Youngs, 22 Joe Marchant, 23 Joe Cokanasiga