The Newcastle forward came from the bench in the 59th minute at the Aviva Stadium, with his side already 2-1 up.
And it didn't take long for him to set up Ireland's third goal. It was his through ball which allowed fellow substitute James McClean to finish beyond visiting goalkeeper Esteban Conde with 14 minutes left to play.
Murphy had started for the Republic on Thursday as they took on Mexico in New Jersey. He came off after 64 minutes as Martin O'Neill's men lost 3-1.
Rob Elliot - who had been named in an initial 37-man party last month - did not feature in either game.
Republic of Ireland are currently second in Group D as they look to qualify for the 2018 World Cup, and victory against Austria in Dublin on Sunday would further enhance their hopes of reaching the finals.
USA are also eyeing a place in Russia next summer and they prepared for Thursday's qualifier against Trinidad & Tobago with a 1-1 friendly draw against Venezuela in Utah on Sunday.
DeAndre Yedlin earned his first cap of 2017 and played for 90 minutes at right-back, before being replaced by Graham Zusi in stoppage time.
Yedlin has not been included in coach Bruce Arena's 40-man preliminary squad for the 2017 CONCACAF Gold Cup, which takes place in July.
On Friday, Florian Thauvin - who spent last season on loan with Marseille - made his senior international debut as a late substitute for France as they won 5-0 against Paraguay.