Ollie Watkins and Curtis Jones were on the scoresheet either side of an own goal from Greece goalkeeper Odysseas Vlachodimos, with the victory leaving the Three Lions top of Group 2 of League B on goal difference.
Lee Carsley's side will top the section and earn promotion to League A providing that they beat Republic of Ireland on Sunday night, but a draw or a defeat would open the door for Greece to return to the summit.
Here, Sports Mole takes a look at how each player performed in the Nations League contest.
Greece player ratings vs. England: Vangelis Pavlidis unable to repeat previous heroics
GOALKEEPER
Odysseas Vlachodimos- 6/10
Made a super save early in the second period to keep out a strike from Rico Lewis, and he was incredibly unfortunate with England's second goal before being beaten for the third. Was not to blame in any way for Greece's three-goal loss.
DEFENCE
Lazaros Rota - 6/10
Can be relatively pleased with how he managed Anthony Gordon for long stages of the contest, but England finished the stronger, and the right-back struggled to deal with the away side's quality off the bench.
Konstantinos Koulierakis - 6/10
Will have been pleased with a lot of his work on the night, as England found it difficult to carve out chances for long spells, but he was ultimately a part of Greece defence that conceded three times.
Konstantinos Mavropanos - 6/10
Was impressive in the first period, with Greece looking to overcome the disappointment of the early goal, and he did make some vital challenges and interceptions over the course of his 90 minutes on the field.
Kostas Tsimikas - 6/10
Should have levelled the scores shortly before the 30-minute mark, but his close-range effort was kept out by Jordan Pickford. Found it difficult against the lively Noni Madueke and was replaced in the 56th minute.
MIDFIELD
Manolis Siopis - 6/10
Was the fifth and final Greek player to be substituted against England, and he tired in the second half after a positive first period.
Christos Zafeiris - 6/10
Will have been pleased with a lot of his work against England, especially in the second period, but England did have a lot of joy through the middle of the pitch in the latter stages of the contest.
Anastasios Bakasetas - 5/10
Just could not get into the match, with England dominating the ball for long spells, and it was not too much of a surprise when he was a part of a triple change for the home side in the 56th minute.
ATTACK
Georgios Masouras - 6/10
Like a number of his teammates, found it difficult in the first period, but he did have more of an influence at the start of the second half before being replaced in Greece's fourth change of the match in the 70th minute.
Vangelis Pavlidis - 5/10
Was excellent in the reverse fixture at Wembley, scoring twice in a 2-1 Greece win, but the striker found it incredibly difficult to make his mark on Thursday night and was replaced just before the hour mark.
Christos Tzolis - 6/10
Was the only one of Greece's four attacking players who started the match to play the full 90 minutes, and he was busy with his work, but the 22-year-old did not have any clear openings in Athens.
SUBSTITUTES
Dimitrios Giannoulis - 6/10
Was introduced as part of a triple change, and the 29-year-old showed some nice touches during his time on the field, but he was unable to prevent Greece from suffering a heavy home defeat.
Fotis Ioannidis - 7/10
Had a glorious chance to level the scores shortly after being introduced, but the striker saw his effort kept out by Pickford; was comfortably Greece's biggest threat off the bench on Thursday night.
Dimitrios Pelkas - 6/10
Only had one shot during his time on the field, but he did produce one key pass, and Greece looked a threat when they managed to feed him in wide areas, which did not happen as often as the home fans would have wanted.
Giannis Konstantelias - 6/10
Finished with a pass success rate of 88%, with the substitute neat and tidy in possession of the football, but he did not really cause England any harm after being introduced in the 70th minute.
Petros Mantalos - 6/10
Had the difficult task of making an impact shortly after England had scored a second, and Greece were simply unable to launch a response in the latter stages of the contest.
England player ratings vs. Greece: Debutants make their mark for Three Lions
GOALKEEPER
Jordan Pickford - 8/10
Booked in the first period for taking too long with a goal kick and then made an outstanding save to deny Tsimikas shortly after. Made another brilliant stop to keep out an attempt from Ioannidis in the second half, and he was England's best player in Athens.
DEFENCE
Kyle Walker - 7/10
Started at right-back before being switched into the middle of the defence for the second period, and the 34-year-old used all of his experience to make it difficult for Greece's forward players.
Marc Guehi - 7/10
Another steady performance from the centre-back, who will surely not be at Crystal Palace for too much longer, with a number of major clubs said to be interested in securing his signature.
Ezri Konsa - 6/10
Was solid in the opening 45 minutes of the contest, with Greece struggling to make their mark, but he was then somewhat surprisingly replaced at the half-time interval by Lewis Hall.
Rico Lewis - 6/10
Started at left-back before switching to right-back at the interval - might have scored early in the second period, but his powerful drive was kept out by the home side's goalkeeper.
MIDFIELD
Conor Gallagher - 6/10
Was busy with his work, as expected, with the Atletico Madrid midfielder certainly covering the ground, but interim head coach Carsley will have wanted to see a little bit more from him in possession of the ball.
Jude Bellingham - 7/10
Hit the post with a header early in the second period, and he started to have a big influence as the match progressed, playing a key role in England's second of the match in Athens.
Curtis Jones - 8/10
Excelled on his debut for England, with the Liverpool midfielder calm and composed in possession of the ball, while he scored an excellent third late on by flicking a cross from Morgan Gibbs-White into the corner of the net.
ATTACK
Noni Madueke - 7/10
Set up Watkins to make it 1-0 in the early stages, and the Chelsea attacker was a big threat in the first half, but he faded after the interval and was replaced by Jarrod Bowen in the 66th minute.
Ollie Watkins - 8/10
Was challenged by Carsley to 'become a leader' after being named in the side ahead of Harry Kane, and the Villa forward took his chance by scoring early on, before being replaced by the Three Lions captain in the 66th minute.
Anthony Gordon - 6/10
Had some mazy runs in the early stages of the contest, with Greece finding it difficult to deal with his pace, but there was not much of an end product from the Newcastle United forward, who was replaced by Morgan Rogers as part of a triple change.
SUBSTITUTES
Lewis Hall - 7/10
England had a lot more balance when the 20-year-old was introduced for his debut at the interval; Hall was always willing to take the ball in tight areas and also excelled defensively in the second half of the contest.
Harry Kane - 6/10
There was no space for Kane in the starting lineup in Athens, with Watkins preferred through the middle, and the Bayern Munich striker found it difficult to make his mark after being introduced off the bench.
Morgan Rogers- 6/10
Came on for his debut in the 66th minute of the match and showed his quality with a couple of powerful runs in the latter stages; there could be a role for him under incoming head coach Thomas Tuchel.
Jarrod Bowen - 6/10
Was involved in England's third, and he certainly played his role in the Three Lions finishing strongly on Thursday night.
Morgan Gibbs-White- 7/10
Set up Jones to score England's third in the latter stages with a clever pass, and his direct running caused Greece all sorts of problems during an impressive cameo.