With the help of former England Under-21 boss Stuart Pearce, we pick out five reasons why Aidy Boothroyd should be encouraged by this victory...
England did not begin their U21 campaign as sharply as they would have liked.
Slovakia are top of Group A, two points ahead of England, after beating Poland 2-1 on Friday while the Young Lions drew their opener with holders Sweden 0-0.
But there was little serious threat from England despite plenty of possession - similar to the Sweden game - with only Chalobah's long-range effort dribbling wide.
Boothroyd said: 'It's knockout football now without a doubt. Having scored over 2.5 goals per game in qualification and failed to score just once in their last 13 fixtures, they should certainly play their part in an entertainingly end-to-end clash. "We've got to win". We handled that after going a goal down.
Even another draw could leave the Young Lions staring elimination in the face, and you can get odds of 13/5 (3.60) on them enduring another frustrating stalemate at the Kolporter Arena.
"The formation he picked with Redmond being a bit closer to him, I'm not sure whether it really, really worked. It felt like a home game", he said. Indeed, he was a reassuring and vocal presence in the England box as Slovakia put pressure on Boothroyd's team in the final stages. Chelsea forward Tammy Abraham was involved in England's victor, holding the ball up to set the side on their way to a quick counter-attack, and his pace and strength are considerable assets. "There were two individual errors which resulted in goals".
"It's really helpful having them here", Boothroyd said.
It was a response England desperately needed and their drastic improvement continued after 61 minutes when Redmond won it.
"I thought Alfie Mawson and Calum Chambers were fantastic today", he added. What we're good at is getting it off the lines and playing in pockets.