England had to hold out against Serbia, with Jude Bellingham's early goal proving enough for the Three Lions to claim a 1-0 win on Sunday.
That kick-started their Group C campaign, and a win over Denmark, who drew 1-1 with Slovenia earlier in the day, will see England progress to the last 16.
Elsewhere, the Netherlands overcame Poland 2-1 thanks to Wout Weghorst's late strike.
Using Opta data, we provide a run-down of the best statistics from day three of Euro 2024.
Serbia 0-1 England: Bellingham the main man for clean sheet kings
England were not exactly free-flowing for much of their clash with Serbia, but Gareth Southgate's team got the job done.
Bellingham was his hero, as he became just the second player ever to score at both the World Cup and Euros before turning 21, after compatriot Michael Owen.
Indeed, Bellingham is the first player to score for the Three Lions at both the World Cup and European Championships while playing his club football outside of England.
Finally, he became the first player to score for England at both the World Cup and Euros while playing his club football outside of England.
Yet it was at the other end that England had to hold their nerve.
Their defence has been questioned ahead of Euro 2024, but England have now kept a clean sheet in each of their last five group stage matches at the European Championships, the longest such run in the competition's history.
Indeed, England have won their opening game in all four of their major tournaments played under Southgate (Euro 2020 and 2024, World Cup 2018 and 2022), just one fewer such victory than across their other 23 major tournament appearances (W5 D11 L7).
Jordan Pickford pulled off a fine save late on to deny Dusan Vlahovic. The Everton star was making his 20th appearance for his country at a major tournament, a joint record for a Three Lions goalkeeper, matching Peter Shilton.
England would have been home and hosed if Harry Kane had not seen a header tipped onto the crossbar. The Bayern Munich star was making his 23rd appearance at a major tournament, seeing him become the outright leader in that regard for the Three Lions.
It was by no mean's a classic. In fact, this game featured just 11 shots, which is the lowest on record in a Euros game.
Slovenia 1-1 Denmark: Eriksen runs the show but Janza haunts the Danes
Christian Eriksen put the traumatic events of Euro 2020 firmly behind him as he scored in Denmark's opening match against Slovenia.
That was the 32-year-old's first goal at the Euros, as he became the oldest Dane to score for the nation at the tournament.
Eriksen created seven chances from set plays versus Slovenia, the most by a player in a game at the Euros since Scotland's Gary McAllister in 1992 v Germany (eight).#
Ultimately, though, Denmark could not get over the line, with Erik Janza rifling in a 77th-minute equaliser.
Janza has now scored three goals for Slovenia (11 appearances) with all three of his goals coming in competitive fixtures and with two of his three goals coming against Denmark.
Kasper Schmeichel may well have saved Janza's shot if it had not had taken a deflection on its way through.
Schmeichel, at the age of 37 yers and 224 days, became the second oldest player to play for Denmark at the European Championship finals (behind Morten Olsen - 38y 308d) and the oldest goalkeeper, overtaking his father Peter (36y 216d).
Slovenia are yet to win a match at the Euros (D3 L1), with their four fixtures the most any nation has played in the competition without recording a single victory, but this result keeps their hopes firmly alive.
Remarkably, all 10 of Denmark's starting outfielders recorded a shot in this match, only the third time a team has seen each of their outfield starters do so on record at the Euros (since 1980) after England v Spain in 1996 and the Netherlands v Italy in 2000.
Defender Andreas Christensen completed all of his 89 passes, meanwhile. It is the most passes any player has made while maintaining a 100 per cent accuracy in a match on record at the Euros.
Poland 1-2 Netherlands: Weghorst makes his point
Former Manchester United attacker Weghorst was not happy to be left out of Ronald Koeman's line-up, but he made sure to make his mark when he came on against Poland.
Weghorst scored the fastest goal by a Netherlands substitute at the European Championships, netting the winning goal of the game just two minutes and 18 seconds after coming off the bench.
His winner came after Cody Gakpo had restored parity in Hamburg. The Liverpool forward has scored in all four of his group stage starts for the Netherlands at major tournaments, and has now found the net in his first start at both the World Cup and European Championships.
Adam Buska put Poland ahead in the 16th minute, becoming just the fourth player for the country to score on his debut at the European Championships, after Robert Lewandowski (2012), Arkadiusz Milik (2016) and Karol Linetty (2021).
The Netherlands were ultimately decent value for their win, having had 21 shots – their most in a game at a major tournament (World Cup/EUROs) since 2012 against Denmark (32), although they did only accumulate 1.47 expected goals.
Chile 0-1 Argentina: Super sub Martinez sends La Albiceleste through to Copa America quarter-finals
Lautaro Martinez struck a dramatic late winner as Argentina beat Chile 1-0 to secure their place in the Copa America knockout stages with a game to spare.
The reigning champions looked like they would have to settle for a point on a frustrating night at the MetLife Stadium, having failed to turn their superiority into the game's opening goal.
But substitute Martinez, who also netted from the bench in his nation's opener against Canada, finally broke Chile's resolve when he lashed home two minutes from time.
It moved Lionel Scaloni's side onto six points at the Group A summit - three points ahead of Canada, who beat Peru 1-0 earlier in the day - meaning a draw against Peru in their final game will be enough to secure top spot.
Argentina dominated the first half with 13 unanswered shots, yet just three of those were on target. One of them saw Julian Alvarez fire straight at Claudio Bravo from close range in the 22nd minute.
Lionel Messi also went close to scoring in the 36th minute. La Albiceleste's skipper let fly with a fizzing 25-yard attempt that clipped the outside of Bravo's left post, while Erick Pulgar almost turned Nahuel Molina's cross beyond the Chile goalkeeper two minutes later.
La Roja had Bravo to thank for keeping Argentina at bay, as the reigning champions continued to carry the greater attacking threat after the break.
The veteran stopper beat away Molina's fierce strike within five minutes of the restart, and just after the hour mark, he produced a superb reflex save to tip Nicolas Gonzalez's drive onto the crossbar.
With the breakthrough still eluding the world champions, Scaloni bolstered his attack by introducing Angel Di Maria and Martinez for the final 17 minutes.
Chile had increased their own attacking threat by registering their first attempts on goal in the contest, with Rodrigo Echeverria calling Emiliano Martinez into action on both occasions.
Yet, there was to be a late twist in Argentina's favour when an 88th-minute corner broke kindly for Martinez, who reacted the quickest to fire into the roof of the net and send La Albiceleste through to the quarter-finals.
Persistence pays dividends for Argentina
The recent history books would suggest Argentina should fancy their chances against Chile.
This is epitomised by the fact they are now unbeaten after 90 minutes in the last 13 meetings, winning eight of those, but that does not tell the full story.
Seven of those eight victories have only been by a single-goal margin and, of course, they lost on penalties in the Copa America final showdowns of 2015 and 2016.
Though they dominated most of this contest and registered 22 shots to their opponents' three, just the one goal was enough once more - with both of Martinez's strikes from the bench in this competition coming in the 88th minute.
Argentina progress to the Copa America knockout stages for a 14th consecutive time, excluding when they withdrew from the 2001 tournament.
Toothless La Roja resistance finally broken
Chile looked set to frustrate Argentina once again at the Copa America, and hold out for a second successive clean sheet.
Their defensive resolve - along with an inspired performance by Bravo between the sticks - looked like it would remain firm and keep the reigning champions at bay, until Martinez's late intervention.
What will be more concerning for La Roja is the fact they have now gone four successive Copa America matches without scoring, while having to wait until the 72nd minute for their first attempt on goal today.
That is something they need to address quickly ahead of their crucial final Group A clash with Canada, in which a victory could still see them snatch second place and a quarter-final spot.
Southgate urges England supporters to 'stay with the team' amid Euro 2024 criticism
Gareth Southgate pleaded for England's supporters to "stay with the team", after venting their frustration following the goalless draw with Slovenia.
The Three Lions advanced to the Euro 2024 knockout stages as Group C winners, despite winning just one of their opening three games and scoring two goals.
Southgate's side, who came under scrutiny following their 1-1 draw with Denmark, did little to silence those critics with another underwhelming performance against the Slovenians.
Despite dominating large periods of the contest with 74% of possession, it yielded an expected goals (xG) tally of just 0.87, with the front three of Harry Kane, Bukayo Saka and Phil Foden registering just two shots on target between them.
Sections of England fans jeered their team at the final whistle, while hurling empty drinks cups in the direction of Southgate as he applauded them.
The Three Lions boss empathised with the supporters, but urged them to point the finger of blame at him, rather than his players.
"I understand it. I'm not going to back away from it," he told reporters during his post-match press conference. "The most important thing is the supporters stay with the team.
"I understand the narrative towards me, and that's better for the team than it being towards them. But it is creating an unusual environment to operate in. I've not seen any other team qualify and receive similar.
"[The players] kept composure in a game where they've come into a really challenging environment. Of course, we'd love a couple of goals that sends everybody home happy. But we were definitely an improvement on what we did in the last game."
"I think the changes we made had a positive effect on the game tonight. We weren't able to find the right pass, the final finish. But we are improving."
Despite the disappointment at their performance levels, England have managed to avoid the half of the draw that includes the likes of France, Germany, Spain and Portugal.
The Three Lions will play either the Netherlands, who finished third in Group D, or Group E's third-placed side in the round of 16 in Gelsenkirchen on Sunday.
And Southgate knows a positive atmosphere within the camp will be crucial as the Euro 2020 finalists target another deep run in this competition.
"You never want to look back having not topped the group and spiral into tough matches where people can then accuse you that, because you didn't win the group, you've ended up with a tougher draw," he added.
"We have made England over the last three or four years fun again. I think it has been enjoyable for the players, and we have got to be very, very careful that it stays that way."
Denmark coach Hjulmand ready to go toe-to-toe with Euro 2024 hosts Germany
Denmark head coach Kasper Hjulmand is relishing the opportunity of facing Euro 2024 hosts Germany in the knockout stages of the tournament this Saturday.
The Danes concluded their Group C campaign with a goalless draw against Serbia in Munich, finishing second behind England in the standings.
"The last seven, eight minutes (against Serbia) were just defending, so I think our defence was really good, Hjulmand said after the game.
"We had to fight through the game at the end. But I think we showed character and there are so many things from the game that I'm happy about.
"There are a few things in the attack that we have to tweak in order to succeed but I know that we can we can do that. We have some great players there."
Denmark drew all three of their group games, finishing ahead of Slovenia based on their disciplinary record, ultimately coming down to Milivoje Novakovic, a member of Matjaz Kek's coaching staff, being shown a yellow card against the Danes.
It sets up a meeting with Germany, a side they have failed to beat in their last four meetings, with their last triumph coming in an international friendly in March 2007.
"I really love football here in Germany and playing against Germany with the Danish team, it can't be better, I can't wait. It's a great team. But we're a great team as well. And when we play the big nations, we always step up," Hjulmand said.
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