Alex Bangura comes in at left-back for Targett, one of two changes.
Jeremy Sarmiento also starts, replacing Dael Fry, with Kim Hellberg switching to a back four.
It means Callum Brittain, Luke Ayling, Adilson Malanda and Bangura start in the defence.
Aidan Morris and Alan Browne start in midfield, with Sarmiento and Riley McGree supporting David Strelec and Tommy Conway.
Targett is missing from the squad after being forced off in the second half of Friday's defeat to Millwall. Fry is among the substitutes. Sontje Hansen also returns to the squad on the bench after missing Friday's game.
MIDDLESBROUGH: Brynn, Brittain, Ayling, Malanda, Bangura; Browne, Morris, Sarmiento, McGree, Strelec, Conway
SUBSTITUTES: Wildsmith, Fry, Gilbert, Munroe, Sene, Edmundson, Hansen, McCabe, Ibeh
SWANSEA: Vigouroux; Parker, Cabango, Burgess, Tymon; Fulton, Franco, Cullen; Eom, Widell; Vipotnik.
SUBSTITUTES: Fisher, Stamenic, Yalcouye, Nunes, Walta, Santos, Ward, Idah, Ronald.