England are now playing Costa Rica in their final warm-up match before the 2018 World Cup.
Roy Hodgson's already-eliminated side brought the curtain down on their awful finals foray with a lifeless goalless draw in Belo Horizonte.
England beat Nigeria 2-1 at Wembley on Saturday and will face a tricky test against fellow-qualifiers Costa Rica, who reached the quarterfinals four years ago in Brazil.
The Elland Road crowd chanted "football's coming home" in a bright start punctuated by flashes of impressive team interplay and skill.
Rashford, who impressed throughout with his speed and control, fired England ahead in the 13th minute, unleashing a dipping drive from the right which flew past Costa Rica keeper Keylor Navas.
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The Manchester United striker, playing alongside Jamie Vardy in attack, was the star of the first hour at Elland Road and capped his performance with a spectacular 25-yard strike.
Tasked with leading the line Rashford, partner-in-crime Jamie Vardy was almost in for a second but was well thwarted by Navas.
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After the break, Jordan Henderson forced a fine save out of Navas with a blast from the edge of the box and defender Harry Maguire had a header cleared off the line by Bryan Oviedo.
Kieran Tripper was amongst them and sent a free-kick just wide, with Danny Rose - the subject of so much pre-match attention after speaking candidly about his depression - directed into the side netting.
Hopefully it will be the 4-4-2 in a bar beat of Terrier Brass that will inspire England to success against Costa Rica and then the rest of the world in Russian Federation in the next month. Alex Iwobi cut the lead in half but it wasn't enough as England emerged victorious at the final whistle.