Marcus Rashford put England on the brink of World Cup qualification after scoring the winner in a 2-1 victory over Slovakia on Monday night.
Defeat would have seen Gareth Southgate's side slip to second place in Group F with two games to play and Stanislav Lobotka's goal after two-and-a-half minutes prompted concern among the 67,823 supporters at Wembley Stadium.
And that means England need just two points from their remaining fixtures against Slovenia and Lithuania to guarantee a place at next summer's World Cup finals in Russia.
Lobotka robbed the Manchester United forward 25 yards from goal and shared the ball with Adam Nemec, who clipped a clever pass over the England defenders back to his team-mate to finish brilliantly past Joe Hart.
England were visibly rattled and laboured for much of the first half, but found an equaliser in the 38th minute. It came from a corner, which was curled by Rashford low to the feet of Dier at the front post and the Tottenham midfielder hooked a first-time shot above Lobotka on the goal-line and into the roof of the net.
England might have been reduced to 10 men on the stroke of half-time when last man Kyle Walker appeared to trip Vladimir Weiss in full flight on the edge of the area, but the referee felt the defender won the ball, much to the frustration of the Slovakia players.
And England capitalised on their fortune as Rashford put them ahead on 59 minutes. Following a neat exchange between Dele Alli and Jordan Henderson, the 19-year-old struck an unstoppable low shot across goalkeeper Martin Dubravka from the edge of the area.
Slovakia had limited opportunities to score a second as Nemec's close-range volley was beaten away by Hart and Tomas Hubocan wastefully bounced a shot over the bar - and they will now need to avoid defeat in their next match at Hampden Park to prevent Scotland going above them into a play-off spot.
England's night might be tarnished if UEFA decide to punish Dele Alli for a crude gesture made towards the referee after he felt he was fouled, but Southgate knows victory against Slovenia next month will secure a passage to Russia after another tenacious, if unconvincing, qualifying display.