They got their reward when Swansea City’s Alfie Mawson netted the equaliser before Redmond struck the winner via a wicked deflection.
And England held on to remain in contention for a semi-final spot, either as group winners or the best runner-up, going into Thursday’s clash with Poland, who needed a penalty in injury time to rescue a 2-2 draw with Sweden in the day's other group match.
England know a victory over the host nation in Kielce on Friday will see them qualify for the last four with Slovakia and Sweden both needing a win to remain alive in their bid to claim the best runner-up spot from the three groups.
Slovakia's goalkeeper Adrian Chovan (R) catches the ball next to England's forward Tammy during the UEFA U-21 European Championship Group A football match Slovakia v England in Kielce, Poland on June 19, 2017
Image credit: Getty Images
Can England U-21s go all the way? Not on the basis of their performances against Sweden and Slovakia. For 45 minutes they were woeful against the eastern Europeans but vastly improved after the break after a tweak in tactics. In comparison to Spain and Portugal’s display, Boothroyd’s side have a long way to go to look like serious tournament contenders.
MAN OF THE MATCH
Nathan Redmond(Southampton): The winger improved as the game wore on and showed his seniority by urging his team-mates to keep their composure on the ball. He did well to make his goal and was more direct than the other midfielders.
23’ - GOAL FOR SLOVAKIA! The corner is floated to the near post and Chrien evades Holgate and glances his header into the corner.
36’ - CHANCE! Chalobah tees up Swift who curls in a shot from 20 yards with little backlift that drifts over the bar.
45’ - GOOD STOP! Ward-Prowse steps up and curls the free-kick over the wall which Chovan tips over the bar.
49’- GOOD SAVE! Redmond cuts inside in the area and fires in a shot which Chovan does well to parry at his near post.
50’ -GOAL FOR ENGLAND! Mawson scores at close range. The corner was played back into the box by Murphy, Mawson's first shot was parried and he slotted in the rebound.
61’ - GOAL FOR ENGLAND! Redmond cuts inside and scores with a deflected effort which flies into the top corner after a brilliant ball from Ward-Prowse.
65’ - PENALTY APPEAL! Slovakia are furious after claiming a cross from the left was blocked by Murphy's arm, replays showed it hit his left arm as he turned his head away from the ball.
Slovakia's defender Martin Valjent (L) and England's midfielder Nathan Redmond vie for the ball during the UEFA U-21 European Championship Group A football match Slovakia v England in Kielce, Poland on June 19, 2017
Image credit: Getty Images
England U-21s have seven victories from their last ten games.
Nathan Redmond scored his tenth goal at Under-21 level.