The Manchester United teenager scored inside the first three minutes at the Stadium of Light to continue a remarkable run of form in 2016, in which he also scored on his Europa League and Premier League debuts.
With concerns over a calf problem for Liverpool's Daniel Sturridge, Rashford's performance has boosted his chance of making Roy Hodgson's final 23-man squad to travel to France for the finals next month.
And Sturridge's club-mate Henderson, who completed 90 minutes for the first time since recovering from a knee injury, is confident Rashford would have no fear of performing on one of the biggest stages in international football.
"It's incredible, really, isn't it?" he told ITV after the match, which was decided by a fine Wayne Rooney strike. "It's just the season he's been having. He's got no fear, wants the ball all the time and runs in behind, and it's a great finish.
"He's done everything. Good on the ball, good movement, his finishing is good. He just needs to continue to work and I'm sure he'll be a big player for United and England.
"He made an impact on his debut so I don't think he'll fear anything. If he's given the opportunity I'm sure he'll do very well."
Henderson was disappointed with England's first-half display in particular against Ange Postecoglu's side and concedes there are concerns to address before their final warm-up match with Portugal on June 2.
"It was a tough 90, there's a lot of things I can do better, but it's my first start for a long time," added the Liverpool captain.
"We were disappointed at half-time, we didn't dominate as we wanted. There's one or two things we need to work on."