Former captain Contepomi, a veteran of four World Cups, is set to win his 87th cap, one more than Lisandro Arbizu and Rolando Martin, in what is likely to be the 36-year-old's international farewell at inside centre in place of Santiago Fernandez.
Horacio Agulla, who has two World Cups to his name, comes in on the right wing in place of Lucas Gonzalez Amorosino, who drops to the bench with Fernandez.
"Both Felipe and Horacio are players of great experience who bring a lot to the team," Phelan said.
Argentina are looking for their first win in two Rugby Championships and a narrow 14-13 loss to Australia in Perth last month has led to speculation this might be the Pumas' big chance.
"We've got to be calm and confident in what we've been practising," Phelan said.
"We did a lot of good things against New Zealand, above all in the first half, and we're looking to prolong that over a longer period," he added.
Australia have struggled to field a settled side this season and lost all their matches until the win over the Pumas with the match at the Gigante de Arroyito football stadium a wooden spoon decider.
However, Phelan is not being lured into a false sense of security.
"Australia are a very complete team with a good pack of forwards and a variety of options in the backs with fast and agile players who play good rugby," he said.
"They are the third best team in the world and it will surely be a very hard fought match in which we must keep our shape and defend well when they have the ball, as we did against New Zealand."
Team: 15-Juan Martin Hernandez, 14-Horacio Agulla, 13-Marcelo Bosch, 12-Felipe Contepomi, 11-Juan Imhoff, 10-Nicolas Sanchez, 9-Martin Landajo; 8-Juan Manuel Leguizamon, 7-Pablo Matera, 6-Juan Fernandez Lobbe (captain), 5-Patricio Albacete, 4-Julio Farias Cabello, 3-Juan Figallo, 2-Eusebio Guinazu, 1-Marcos Ayerza
Replacements: 16-Agustin Creevy, 17-Nahuel Lobo, 18-Juan Pablo Orlandi, 19-Manuel Carizza, 20-Benjamín Macome, 21-Tomas Cubelli, 22-Santiago Fernandez, 23-Lucas Gonzalez Amorosino