But the night belonged to Rashford, who netted three minutes into what was only his 19th professional match, stroking the ball first time past goalkeeper Matt Ryan after creating space inside the area at Sunderland's Stadium of Light.
Rashford, who also scored on his United debut in February, could have had a second goal minutes later and produced an assured performance before coming off on the hour.
Manager Hodgson praised his debutant but refused to confirm whether Rashford will be in the trimmed down 23-man squad that must be named before Tuesday.
"It was fantastic, he did very well and I am pleased for him on his debut," Hodgson said. "He would not be out of place in anyone's 23."
Rashford probably only started against Australia because of an injury to Daniel Sturridge, but Hodgson said he was hopeful the Liverpool striker will recover sufficiently to train with the squad on Monday.
"If he does, the calf injury will not be a reason to leave him out of the 23," said Hodgson. "None of those decisions (about who to leave out) will be injury-related."
Rooney scored a record-extending 52nd goal for his country with a fine strike 10 minutes after the break.
(Reporting by Neil Robinson, editing by Ed Osmond; Editing by Ken Ferris)
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