Emil Forsberg's double was cancelled out by two Robert Lewandowski goals before Viktor Claesson struck in added time to seal first place in Group E.
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An added-time goal from Viktor Claesson gave Sweden first place in Group E and ended Poland's hopes of progressing to the round of 16 in a five-goal thriller in Saint Petersburg.
Match in brief
Sweden's place in the knockout rounds was already assured, but they still began at breakneck speed and were ahead just over a minute in, Emil Forsberg – scorer of their penalty winner on Matchday 2 – firing in from the edge of the penalty area after good work from Alexander Isak.
Poland responded well to the early setback and somehow failed to draw level when Robert Lewandowski headed a corner against the crossbar and then repeated the trick from close range after latching onto the rebound. Robin Olsen stretched to tip over a stinging Piotr Zieliński drive just before the break and had to be similarly alert to palm away another long-range effort from the same player not long after the restart.
The Sweden goalkeeper then kept out a low Grzegorz Krychowiak effort and his side made those saves count just before the hour, substitute Dejan Kulusevski carrying the ball from from halfway before squaring for Forsberg to place a low shot just inside the post. A fine Lewandowski goal quickly halved Poland's arrears and inspired his team to throw more men forward, and six minutes from time the ball fell to the striker inside the area to level matters.
That was still not enough for Poland, who needed one more goal to go through, and were increasingly obliged to commit players to attack. Instead it was Sweden who snatched victory, substitute Claesson giving them first place in the section with a cool finish in the 94th minute.
Star of the Match: Emil Forsberg (Sweden)
"He scored two goals and orchestrated Sweden's victory."
Mixu Paatelainen, UEFA Technical Observer
Sujay Dutt, Sweden reporter
Poland were the team who needed to win, but instead it was Sweden that got off to a roaring start thanks to Forsberg's low effort. They then took their foot off the gas and were fortunate to still be in the lead at the break. Substitute Kulusevski's pace and vision set up Forsberg’s second and Sweden appeared to be heading for the top of Group E. Lewandowski's double looked like it would prove otherwise, but Claesson's late winner means Sweden go into the round of 16 in good spirits.
Piotr Koźmiński, Poland reporter
Before this game, Poland's coach and players had underlined how difficult a task they faced, and the opening two minutes showed the truth of that. Poland's defensive troubles proved too much to overcome; the consolation was yet another Lewandowski masterclass. With five goals, he's now Poland's all-time top scorer in EURO final tournaments.
Emil Forsberg, Sweden forward: "It was a crazy start. It meant that they were more a little more desperate than us. They created chances, could have scored, and we had a bit of luck. At 2-0, the game should be over, but they equalised, and their goals came a little too easily. But then we got the third, and now it's just pure happiness."
Janne Andersson, Sweden coach: "[Forsberg]'s a bit calmer as a person. He's said himself that he feels more harmonious, and he's been better on the pitch. He's always been good with the national team, and it's great he can be the decisive factor for us. Overall we defended well, although in the second half we defended a little too deep. We'll have to look at the game again, analyse it, and see what we can do better."
Robert Lewandowski, Poland forward: "We're sad and disappointed. Maybe we were lacking quality somehow, but we gave all we had. We've been unlucky at this tournament. We had many chances to score but didn't convert enough of them. And our rivals sometimes had half a chance and they scored. I feel this team deserved more; for all that we gave here, the reward is too small."
- Sweden are into the knockout stages for the first time since 2004, when they reached the quarter-finals.
- This is the third time Sweden have topped their group at a EURO, after 1992 and 2004; they were also unbeaten in all three group campaigns.
- Forsberg's goal was timed at 1 minute 22 seconds, making it the second-fastest ever at a EURO.
- This was Sweden's 23rd EURO finals match and only the third they were winning at half-time, after their games against France (1992) and Bulgaria (2004).
- Claesson has now scored ten goals in his 49 Sweden appearances.
- Sweden scored three goals in a EURO finals match for only the second time, the other their 5-0 win against Bulgaria at EURO 2004.
- This was the first time Poland have scored two goals in a EURO finals match in their 14th game.
- Lewandowski has scored 69 goals in 122 appearances for Poland; this was the 17th time that he had scored two or more in an international match.
Sweden: Olsen; Lustig (Krafth 68), Lindelöf, Danielson, Augustinsson; Ekdal, Olsson; S Larsson, Forsberg (Claesson 78); Quaison (Kulusevski 55), Isak (Berg 68)
Poland: Szczęsny; Bereszyński, Glik, Bednarek; Krychowiak (Płacheta 78), Klich (Kozłowski 73); Jóźwiak (Świerczok 61), Świderski, Zieliński, Puchacz (Frankowski 46); Lewandowski
Sweden – vs third-place team from Group B or C in Glasgow, 29 June