Clifford, 23, is fit for the second fixture in the 2017 compeition after recovering from a chest injury and will play in the pack while Nowell will feature on the right wing.
"Clifford deserves his starting role. He is a hard-working, young player," Jones said in a Rugby Football Union statement. "He has got a good record against Wales. He had a superb game against them in May, he knows what he is going to expect from Wales and we're looking forward to him making an impact to our back-row play."
Nowell, 23, was impressive after coming on as a 69th-minute replacement against France. One burst paved the way for the decisive try by fellow substitute Ben Te'o.
"Nowell starts this week, with Jonny May changing to a finisher," Jones added. "Jack has an excellent work-rate and he's a guy that carries through the line, which will be important for us."
Jones said he accepted responsibility for what he described as an awful performance against France on 4 February at Twickenham.
England came from behind to win 19-16 to register their 15th consecutive victory. Wales started their Six Nations campaign with a 33-7 win over Italy in Rome on Sunday.
"Playing Wales in Cardiff is one of the biggest games in world rugby and we're excited. These are the games you want to be part of as a player and a coach," the former Australia and Japan boss added.
"We have a young team eager to play well at the Principality Stadium."