Rashford replaced Adam Lallana in the 73rd minute of the Group B clash to make his competitive international debut at the age of 18 years and 229 days, four days younger than Rooney was when he lined up against France at Euro 2004.
His appearance off the bench was another chapter in a remarkable first season for Rashford, who only made his first-team debut for Manchester United in February.
The striker scored twice against Danish side Midtjylland in a Europa League tie, and followed that up with another brace in the Premier League win over Arsenal three days later.
After also scoring the only goal in a derby victories over Manchester City and further strikes in wins against West Ham United, Aston Villa and Bournemouth, Rashford received a first call-up to the senior England squad.
After scoring the opener in a 2-1 friendly win over Australia, Rashford secured his place in the final 23-man squad for the Euros.