There were tributes to George Baldock ahead of the match, with the England-born Greece international tragically losing his life on Wednesday at the age of 31.
Baldock, who joined Panathinaikos from Sheffield United over the summer, qualified for Greece through his grandmother, and he turned out for the national side on 12 occasions.
Greece had an early sighter at Wembley, with Pavlidis curling one just wide of Jordan Pickford's post, before Levi Colwill incredibly cleared an effort from Tasos Bakasetas off the line after the England goalkeeper had lost the ball outside his own box.
Dinos Mavropanos then headed into the England goal from close range, only for the offside flag to come to the home team's rescue during a difficult period for the Three Lions, who looked extremely open through the middle.
Greece took the lead in the early stages of the second period, with Pavlidis showing clever feet inside the England box before smashing the ball past Pickford from close range to score his country's first-ever goal at Wembley.
The visitors again had the ball in the back of the net through Georgios Masouras just before the hour, but the offside flag once again came to England's rescue.
Pavlidis then had one chalked off in the 83rd minute after turning a Christos Tzolis cross into the back of the net, and Greece were finally undone in the 88th minute when Jude Bellingham's powerful drive from distance found a route into the corner, seemingly saving Lee Carsley's side.
Greece were not to be denied, though, scoring a second in the 94th minute through Pavlidis to secure their first-ever victory over England.
The result has left Greece top of Group 2 of League B on nine points from three matches, while England are second, collecting six points from their first three games of the 2024-25 competition.
ENGLAND VS. GREECE HIGHLIGHTS
Levi Colwill clearance vs. Greece
Incredible piece of defending from England's Colwill, as the 21-year-old manages to hook an effort from Bakasetas off the line after Pickford had vacated his goal; what a goal-line clearance!
Dino Mavropanos disallowed goal vs. England
Greece have the ball in the back of the England net in the 11th minute, with Mavropanos heading home from close range, but the centre-back is denied by the offside flag. More defensive concern for England there.
Vangelis Pavlidis goal vs. England (49th min, England 0-1 Greece)
Greece make the breakthrough in the 49th minute, as Pavlidis dances his way into the England box before firing the ball past Pickford, but questions must be asked about the England defending there.
Georgios Masouras disallowed goal vs. England
Greece again have the ball in the back of the net, as Masouras smashes low past Pickford, but the offside flag once again comes to England's rescue, and it remains 1-0 to the visitors.
Vangelis Pavlidis disallowed goal vs. England
Greece have the ball in the back of the England net for a fourth time, but it is again disallowed, with Pavlidis just ahead of the final defender when Tzolis delivered into the box.
Jude Bellingham goal vs. Greece (87th min, England 1-1 Greece)
England level the scores in the 88th minute, with Bellingham striking one into the back of the net from distance; Greece goalkeeper Odysseas Vlachodimos gets a hand on it, but he cannot keep it out.
Vangelis Pavlidis goal vs. England (94th min, England 1-2 Greece)
Incredible scenes here; Greece have won it! The ball breaks for Pavlidis inside the England box, and he smashes the ball into the bottom corner.
MAN OF THE MATCH - VANGELIS PAVLIDIS
Pavlidis made the breakthrough at Wembley with a brilliant goal, and the 25-year-old was a constant threat for the visitors due to his clever movement and ability to keep hold of the ball.
The forward would also have finished with an assist had he not been slightly offside before feeding Masouras, but Pavlidis, who has scored twice for Benfica during the 2024-25 campaign, proved to be the hero in the final exchanges when his second sent the visitors 2-1 ahead in the English capital.
ENGLAND VS. GREECE MATCH STATS
Possession: England 63%-37% Greece
Shots: England 12-12 Greece
Shots on target: England 2-3 Greece
Corners: England 9-5 Greece
Fouls: England 10-14 Greece
BEST STATS
WHAT NEXT?
England's attention will now switch to Sunday's game against Finland, where they will be bidding to return to winning ways in their 2024-25 UEFA Nations League campaign.
Greece, meanwhile, will aim to make it four straight victories in Group 2 of League B when they tackle Republic of Ireland on Sunday night.