The experienced duo are the only two alterations made by coach Eddie Jones from the side that beat Italy 46-15 last weekend, with Harlequins ace Care replacing the injured Ben Youngs and Bath centre Joseph coming in for Ben Te'o, who drops down to the bench.
Care will become the most-capped England scrum-half of all-time during Saturday's contest at Twickenham and he has been handed his chance after Youngs was ruled out for the rest of the tournament with the knee ligament injury he suffered last weekend.
Richard Wigglesworth, who has not featured for England since October 2015, was drafted into the squad following the injury to Youngs and he has been included amongst the replacements.
England have won their last three meetings with Wales, including last year's 21-16 victory in Cardiff, and Jones admits his side are determined to get one over Warren Gatland's team once again this year.
'The team is hugely excited about playing in front of 82,000 fans at Twickenham and we'll be well prepared and ready to go out there and beat Wales on Saturday,' Jones said.
England team to face Wales: 15 Mike Brown, 14 Anthony Watson, 13 Jonathan Joseph, 12 Owen Farrell, 11 Jonny May, 10 George Ford, 9 Danny Care; 1 Make Vunipola, 2 Dylan Hartley, 3 Dan Cole, 4 Joe Launchbury, 5 Maro Itoje, 6 Courtney Lawes, 7 Chris Robshaw, 8 Sam Simmonds.
Replacements: 16 Jamie George, 17 Alec Hepburn, 18 Harry Williams, 19 George Kruis, 20 Sam Underhill, 21 Richard Wigglesworth, 22 Ben Te'o, 23 Jack Nowell.