England dominated the match but their failure to beat Slovakia, who came third and should also go through to the last 16, means they will face the runners-up in Group F.
England made six changes and their new-look team created several chances, with Jamie Vardy, Adam Lallana, Nathaniel Clyne and substitute Deli Alli having efforts to break the deadlock overnight, Australian time.
Despite the roar of their fans, who vastly outnumbered Slovakia’s in the St Etienne stadium known locally as the cauldron, they could not find a way through the Slovak defence.
England have five points, behind Wales, who beat Russia 3-0, on six, and will play their last 16 tie in Nice on June 27.
If England had finished top, they would have played a third-placed team in Paris two days earlier in a location much closer to their training base which would have suited Hodgson.
Slovakia, on four points, must wait to see if they go through as one of the four best third-placed teams.
Hodgson took a major gamble by revamping the side that beat Wales 2-1 last Thursday, including resting captain Wayne Rooney, and saw his team make a bright start.
Vardy posed a constant threat in the first half and full back Clyne, replacing Kyle Walker, regularly troubled the Slovak defence with probing runs down the right wing.
Meanwhile, Wales outplayed Russia 3-0, scoring twice in the opening 20 minutes, as they moved into the round of 16 at Euro 2016 by winning Group B.
Aaron Ramsey, who was named man of the match, dinked the ball over Igor Akinfeev to finish off a counter-attack in the 11th minute and Neil Taylor added a second, also from a counter-attack nine minutes later as Wales took early control.
Russia had no answer to the fast, incisive Welsh breaks and survived several more chances before Gareth Bale scored his third goal of the tournament to become Euro 2016’s top marksman, flicking the third past Akinfeev in the 67th minute.
Wales topped the group with six points, one ahead of England, who finished second after a 0-0 draw with Slovakia.
Chris Coleman’s team will now play one of the third-placed sides in Paris on Saturday with every hope of reaching the last eight, as they did in 1976.
It was a glorious night for Welsh football in what had been described as the country’s biggest game since the 1958 World Cup quarter-final.
Their players and supporters celebrated wildly while Russian fans, who had caused trouble at the end of their first match against England, slunk away.
Russia now go home with much to think about before hosting the World Cup in two years time.
Wales, mostly on the back foot in the previous game against England, rediscovered the attacking brio that had enabled them to beat Slovakia before that.
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