Kriel suffered a hamstring injury in the team's opening Pool B defeat to New Zealand and it has now been deemed he will not recover to feature in the group stage, prompting a switch with Willemse.
Director of rugby Rassie Erasmus said: "Damian would have been more involved with us this year but for injury. He is familiar with our systems and should have no problem slotting in."
He added: "I feel for Jesse. He has been in the matchday 23 for almost every match since I took over and is a model professional. He was a key member of the squad."
Erasmus named his XV to face pool leaders Italy on Tuesday, reverting to 12 of the players who started the game against the All Blacks.
But Tendai Mtawarira, Bongi Mbonambi and Lood de Jager, three members of the pack in a big win over Namibia, have been rewarded for their performances in the second pool match.
They keep their places at the expense of Steven Kitshoff, Malcolm Marx and Franco Mostert, who all drop to the bench.
— Springboks (@Springboks) October 1, 2019
Erasmus selected only two backs among the replacements but revealed he is anticipating "a major forward battle" against Italy.
And with the Azzurri ahead of South Africa with two wins from two, it is absolutely vital there are no slip-ups from the Rugby Championship winners.
"Italy have had their eyes on this match for a couple of years and will have planned and schemed how to bring us down once again," said Erasmus.
"This is a defining match for them and, while we were focusing on the New Zealand game, they will have had their eyes on this one as the key to the quarter-finals for them.
"That means we have to be at our absolute best if we are to beat them. We are at the stage already where there are no second chances. That's a message we have been emphasising to the players this week."
South Africa team: Willie le Roux, Cheslin Kolbe, Lukhanyo Am, Damian de Allende, Makazole Mapimpi, Handre Pollard, Faf de Klerk; Tenda Mtawarira, Bongi Mbonambi, Frans Malherbe, Eben Etzebeth, Lood de Jager, Siya Kolisi, Pieter-Steph du Toit, Duane Vermeulen.
Replacements: Malcom Marx, Steven Kitshoff, Vincent Koch, RG Snyman, Franco Mostert, Francois Louw, Herschel Jantjies, Frans Steyn.
Photo Getty Images Caption: South Africa coach Rassie Erasmus