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Henderson started in place of regular number one David de Gea and kept a clean sheet as United defeated Luton Town 3-0 in the Carabao Cup third round.
After starring on loan at Sheffield United last season, Henderson returned to Old Trafford and signed a five-year contract last month.
The 23 year-old – a product of the club's academy – impressed on his debut at Championship side Luton, producing a fine save to deny Tom Lockyer from close range during the closing stages before Marcus Rashford and Mason Greenwood sealed the victory after Juan Mata's first-half penalty.
Reacting afterwards, Henderson wrote via Twitter: "I dreamt about this my whole life!!
"Unbelievable feeling to make my debut for the club I love! Clean sheet and a win to top it off!!!"
Henderson watched from the bench as United opened its Premier League season with a shock 3-1 defeat at home to Crystal Palace last week.
Ole Gunnar Solskjaer's United travels to Brighton and Hove Albion on Sunday (AEST).