Sale Sharks flanker Curry and Bath back-row Underhill were key components to the England side which progressed to the Rugby World Cup final in Japan last year. Wasps' Jack Willis and Bath second row Charlie Ewels drop out of the squad entirely as a result, with Maro Itoje shifting from the blindside back to lock.
Elsewhere, Jones has promoted first-choice props Mako Vunipola and Kyle Sinckler back into the starting XV, with Ellis Genge and Will Stuart dropping to the bench.
The back-line remains unchanged from England's 40-0 win over Georgia last time out, with Jonathan Joseph ruled fit to start on the wing again despite having limped off with a back spasm last week.
Worcester centre Ollie Lawrence keeps his place at outside-centre in only his second-ever Test start, with Exeter's Henry Slade partnering in midfield.
Experienced out-half George Ford has returned from injury to take his place among the replacements, with Exeter lock Jonny Hill also brought in.
"I've picked the strongest team possible for the most important game of our season," Jones said on Thursday.
"We have the highest respect for Ireland and their coach Andy Farrell. They've had good preparation with two wins and a dominant display against Wales, and we will need to be at our best on Saturday.
"We've trained well this week, we're expecting a tough, physical game against Ireland and we've reflected that in our sessions. We'll look to lift our performance even higher and are looking forward to a really good game of rugby."
England: 15 Elliot Daly, 14 Jonathan Joseph, 13 Ollie Lawrence, 12 Henry Slade, 11 Jonny May, 10 Owen Farrell (c), 9 Ben Youngs; 1 Mako Vunipola, 2 Jamie George, 3 Kyle Sinckler, 4 Maro Itoje, 5 Joe Launchbury, 6 Tom Curry, 7 Sam Underhill, 8 Billy Vunipola
Replacements: 16 Tom Dunn, 17 Ellis Genge, 18 Will Stuart, 19 Jonny Hill, 20 Ben Earl, 21 Dan Robson, 22 George Ford, 23 Max Malins.