The striker lost his man as Slovakia took the lead in the third minute through Stanislav Lobotka.
But from then on Rashford had an impact on every aspect of the game.
The United striker took the corner which Dier slotted home before the teenager slammed home from outside the box to ensure England walked away with all three points.
Dier explained: “Marcus Rashford’s night? It wasn’t so good to begin with but it got better!
“A fantastic show of character after making a mistake to score and then score the winner which got us closer to the World Cup where hopefully he will shine.
Michael Keane – 50/1
“A really important win, it was difficult after starting really poorly but we regained composure.”
Rashford also explained the importance of his first Wembley goal in the victory.
He said: “It was an important goal, we started slowly as a team and me on a personal level too.
“We had to go back to basics and what we had been working on as a team.”
England now need just two points to ensure their place in the World Cup next summer.
The Three Lions have games against Slovenia and Lithuania at the beginning of October to achieve their target.