The Manchester United forward scored a stunning 25-yard strike as the team beat Costa Rica 2-0 at a sold-out Elland Road.
Danny Welbeck headed in the second goal to seal the victory after manager Gareth Southgate rested a host of players including captain Harry Kane.
The friendly was played just 11 days before the Three Lions’ opening World Cup match in Russia against Tunisia.
After the game, Rashford said he believed “anything’s possible” when discussing England’s chances of winning the tournament.
The 20-year-old said: “If everyone goes with that mentality and performs to the best of their ability then we know we’ve got a good chance.
“Anything’s possible so we have to go there with the highest expectations.
“The friendlies have just been showcasing ourselves to the fans how far we’ve come on.
“We know how far in training we’ve come on, especially in the last 18 months, and these games are just an opportunity to show it to everyone.”
Southgate said he was “really pleased” with England’s final World Cup preparations and the squad had avoided any serious injuries.
Asked if he knew his starting 11 players for the opening fixture in Volgograd on 18 June, he replied: “I might sleep on it.”
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England play their other World Cup group games against Panama on 24 June and Belgium on 28 June.
The team are 14/1 with a leading bookmaker to win the tournament, behind the likes of favourites Brazil at 4/1, Germany at 9/2 and France and Spain at 6/1.