Despite the win, it was a largely underwhelming performance from Aidy Boothroyd's side and Martin Chrien's opener looked to have England on the brink of another early European exit.
The Young Lions fought back with two goals in 11 minutes heading into its final group stage clash against host Poland on Friday (AEST).
In the opening stages, England did little to threaten Slovakia despite plenty of possession, with Chalobah's long-range effort dribbling wide.
Slovakia made England pay after 23 minutes, when Chrien got on the end of Albert Rusnak's corner kick, heading past Jordan Pickford.
Murphy replaced Holgate at the break and made an instant impact as he teed up Mawson for the equaliser just five minutes into the second half.
The Norwich winger, playing in an unfamiliar right-back role, crossed for the Swansea defender who tapped in from close range after his initial effort was saved.
It was a response England desperately needed and Redmond found the winner for his side in the 61st minute.