All three were key members of Ireland's World Cup team last year whose dreams of winning the trophy were dashed by the All Blacks in a quarter-final thriller.
Keenan returns after the dynamic fullback took a sabbatical to play for Ireland's sevens team at the Paris Olympics.
Hansen comes back after missing the Six Nations - which saw Ireland retain their title though miss out on repeat Grand Slams - through injury.
His Connacht teammate Aki, whose performances last year earned him a world player of the year nomination, missed the second Test against the Springboks due to a shoulder issue.
Another Connacht man, Finaly Bealham, also starts, the Australia-born prop coming in for the injured Tadhg Furlong.
Jack Crowley has been given the nod by head coach Andy Farrell at fly-half despite Ciaran Frawley being the match winner in South Africa with a last gasp drop-goal in the 25-24 victory which secured a 1-1 drawn series.
Caelan Doris skippers the side, although regular captain Peter O'Mahony is on the bench and can provide an experienced helping hand to the 26-year-old should it be needed.
The Irish and All Blacks will be meeting for the fifth time in just over two years with them tied at 2-2, the Irish having recorded a historic 2-1 series victory in New Zealand in July 2022.
Ireland Team
15 Hugo Keenan; 15 Mack Hansen, 13 Garry Ringrose, 12 Bundee Aki, 11 James Lowe; 10 Jack Crowley, 9 Jamison Gibson-Park; 8 Caelan Doris (capt), 7 Josh van der Flier, 6 Tadhg Beirne; 5 James Ryan, 4 Joe McCarthy; 3 Finlay Bealham, 2 Ronan Kelleher, 1 Andrew Porter
Replacements: 16 Rob Herring, 17 Cian Healy, 18 Tom O'Toole, 19 Iain Henderson, 20 Peter O'Mahony, 21 Conor Murray, 22 Ciaran Frawley, 23 Jamie Osborne