Supporters were fearing the worst when the match went to penalties, and sure enough England's abysmal record in shoot-outs continued as Ashley Young struck the bar and Ashley Cole's kick was saved by Gianluigi Buffon.
The South Americans had been getting away with blatant holding and wrestling at each of England's many corners and the referee's patience finally snapped when Carlos Sanchez hauled down tournament leading scorer Kane once too often.
Colombia conceded 23 fouls as well, 10 fewer than Gareth Southgate's side in a tight encounter, but Falcao believes his team were at a disadvantage because of the United States referee.
Eric Dier scored the winning kick after Jordan Pickford's brilliant save from Carlos Bacca's attempt, with England's first ever World Cup shootout win setting up a meeting with Sweden in Samara on Saturday.
"I think for them, definitely a big moment".
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After spending years seemingly willing the ball in the hole when it mattered most, Woods has lacked that clutch trait this season. Woods, a 14-times major victor , has been stuck on 79 PGA Tour victories - three shy of Sam Snead's record - since 2013.
Another tweeted: "The more I see of Mr Southgate, the more impressive he gets".
"It was a nervous one". I have never been in a situation like that before but I felt like I had to score after the header I missed at the end.
We know Ian Wright was clutching Lee Dixon as it went off in the ITV studios. On top of that, England was knocked out of the 1996 European Championship semifinals and the quarterfinals in 2004 and 2012 on penalties.
That came 22 years ago, against Spain at Euro 96, but it has been otherwise been a tale of woe, with current manager Gareth Southgate famously missing the crucial kick in a defeat against Germany later in the same tournament.
Kane now joins Gary Lineker as the only England player to have bagged six goals at a single World Cup.
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Belgium boss Roberto Martinez was more optimistic, and said the benefit of the extra rest would outweigh any potential negatives. Meanwhile, NAIJ.com had earlier reported that Belgium's opponents, Brazil, defeated Mexico by 2-0 in their last-16 match .
They might have been outnumbered in the stadium but earlier in the day, at Bistro restaurant on one of Moscow's main shopping streets, England's modest following made their presence felt.
"To get knocked down at the end like we did at the end, it's hard to come back from that, " Dier said.
Still, Colombia coach Jose Pekerman wasn't happy with the English approach. I wish I was wrong, but I think from the next match England will be much more careful. Barrios wasn't sent off for the incident, the referee giving opting to give him a yellow card despite not seeing what happened and not consulting VAR.
"I apologise to all the Colombian people, but the players are not to blame - here is a gentleman (FIFA referees boss Pierluigi Collina) who decides to choose a referee who, by googling him, can't be used for a match of this magnitude", Maradona told Venezuelan TV channel Telesur.
The have shown those qualities in this tournament but on Tuesday, under pressure and facing risky players of the ability of Radamel Falcao and Juan Cuardado they also showed they have all the defensive basics in place.
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Ryan Frashure said officers arrived within about 60 seconds and took the gunman into custody without an exchange of gunfire. Press Secretary Sarah Sanders added in a tweet: "Strongly condemn the evil act of senseless violence in Annapolis, MD ".