Lee Carsley's side entered the match knowing that they needed a two-goal success to ensure that they would be at the top of the section heading into their final fixture with Republic of Ireland, and the Three Lions managed to score three unanswered goals.
England made the breakthrough in the seventh minute of the contest, with Ollie Watkins turning a Noni Madueke cross into the back of the net from close range to score his fifth goal in a Three Lions shirt.
Watkins was picked ahead of Harry Kane, who had hit the headlines on Wednesday night when he criticised the players who have withdrawn from the England squad during the current international break.
There had been talk of a potential injury for Kane, but interim head coach Carsley revealed ahead of the match that Watkins was being given the chance 'to become a leader'; he certainly made the most of his opportunity, and the goal would have been a relief, having not scored in his last five games for Aston Villa.
Jude Bellingham headed against the post early in the second period, before Fotis Ioannidis was denied by an excellent save from Jordan Pickford, with Greece coming close to levelling the scores.
England doubled their advantage in the 78th minute of the contest, though, with Bellingham's strike after an excellent run coming off the post before hitting the back of Greece goalkeeper Odysseas Vlachodimos and dropping into the back of the net.
The visitors then made it 3-0 in the 83rd minute, as Curtis Jones scored a debut goal by flicking a cross from Morgan Gibbs-White into the bottom corner.
England are now ahead of second-placed Greece on goal difference, meaning that any win over Republic of Ireland on Sunday would see them top the group and earn promotion to League A, but a draw or a defeat could see them finish second, which would mean a spot in the promotion playoffs.
GREECE VS. ENGLAND HIGHLIGHTS
Ollie Watkins goal vs. Greece (7th min, Greece 0-1 England)
England make the breakthrough in the seventh minute of the contest, and the goal comes from Watkins, with the striker turning a low cross from Madueke into the back of the net from close range; England have struck early in this key Nations League clash.
Odysseas Vlachodimos own goal vs. Greece (78th min, Greece 0-2 England)
England double their advantage in the 78th minute of the match, and it is unfortunate for the Greece goalkeeper, as a strike from Bellingham comes off the post before hitting Vlachodimos and dropping into the back of the net.
Curtis Jones goal vs. Greece (83rd min, Greece 0-3 England)
Jones caps his England debut with a wonderful goal, as the Liverpool midfielder flicks a cross from Gibbs-White into the back of the net, with the Three Lions taking a 3-0 lead in Athens.
MAN OF THE MATCH - JORDAN PICKFORD
Pickford demonstrated on Thursday night why he is England's number one goalkeeper; the Everton man made an excellent save in the first half to deny Kostas Tsimikas, before keeping out Ioannidis in the second period.
The 30-year-old made four saves in total during a brilliant performance between the sticks, and incoming head coach Thomas Tuchel will have no issues when it comes to selecting him, as there is not another English goalkeeper close to him.
GREECE VS. ENGLAND MATCH STATS
Possession: Greece 43%-57% England
Shots: Greece 10-9 England
Shots on target: Greece 5-5 England
Corners: Greece 4-3 England
Fouls: Greece 18-10 England
BEST STATS
WHAT NEXT?
Any win for England over Republic of Ireland at Wembley on Sunday evening would see them finish at the top of the section and earn promotion, but a draw or a defeat would open the door for Greece.
Ivan Jovanovic's side are now second in the section, and they will finish away to Finland on Sunday, looking for a victory and then hoping for a favour from Republic of Ireland in order to finish at the summit.