Rahm has shone for Europe, winning 2 and a half points from three matches.
World number one Scheffler has struggled so far this week, taking just half a point, and was thrashed alongside Brooks Koepka by a record 9 and 7 margin against Ludvig Aberg and Viktor Hovland in Saturday's foursomes.
Rahm and Tyrrell Hatton beat Scheffler and Sam Burns in the first match of the event on Friday.
Donald has put all of his four rookies in the bottom half of the draw as Europe attempt to get the job done early, while USA skipper Zach Johnson has left the out-of-sorts Jordan Spieth, Justin Thomas and Brooks Koepka lower down.
"I like every square inch of our boat; that goes without saying," Johnson said when asked if he had "loaded his boat" for the singles.
"But I do feel like we've got some guys that are in a position and are willing and wanting to be in those positions that is really attractive to me.
"This list really wasn't that difficult, to be honest with you, and they look really good, too."
Koepka, who looked shellshocked on Saturday and was rarely seen on the course supporting his teammates in the afternoon, will have an immediate chance for revenge when he plays Aberg in the seventh game.
Hovland faces Collin Morikawa in the second match, before in-form Justin Rose takes on the USA's Saturday hero Patrick Cantlay.
Rory McIlroy was angered by the behaviour of Cantlay's caddie Joe LaCava on Saturday, saying he wants the controversial scenes on the 18th green to "fuel the fire" for Europe on Sunday.
He will go up against Burns in match four.
Scottish rookie Robert MacIntyre is entrusted with the anchor match for Europe against US Open champion Wyndham Clark.
Rickie Fowler, who has not played for the Americans since Friday morning's opening foursomes, faces Tommy Fleetwood in the penultimate clash.
Schedule for the closing singles session: (tee-off times GMT):
0935: Jon Rahm (EUR) v Scottie Scheffler (USA)
0947: Viktor Hovland (EUR) v Collin Morikawa (USA)
0959: Justin Rose (EUR) v Patrick Cantlay (USA)
1011: Rory McIlroy (EUR) v Sam Burns (USA)
1023: Matthew Fitzpatrick (EUR) v Max Homa (USA)
1035: Tyrrell Hatton (EUR) v Brian Harman (USA)
1047: Ludvig Aberg (EUR) v Brooks Koepka (USA)
1059: Sepp Straka (EUR) v Justin Thomas (USA)
1111: Nicolai Hojgaard (EUR) v Xander Schauffele (USA)
1123: Shane Lowry (EUR) v Jordan Spieth (USA)
1135: Tommy Fleetwood (EUR) v Rickie Fowler (USA)
1147: Robert MacIntyre (EUR) v Wyndham Clark (USA)
