Pickford made a brilliant save to deny a speculative shot from Uribe in the third minute of stoppage time but Mina rose above Harry Maguire to head in the resulting corner to send the game to extra-time.
The England skipper sat at the top of the World Cup goal charts after hitting the net five times in just two matches as the Three Lions booked a last-16 meeting with the South Americans in Moscow on Tuesday.
Los Cafeteros will face Gareth Southgate's side at the Spartak Stadium on Tuesday night, with Sweden or Switzerland awaiting the victor in the quarter-finals. This really is a new England team, however, and at a time when past English teams might have crumbled, this one revived itself to advance. "We know the quality of his finishing, so he's a player that we know all about and we wouldn't judge him on the period he had in the Premier League, that's for sure".
With the likes of Germany, Argentina, Portugal and Spain having already been eliminated from the tournament, the Three Lions now find themselves three games away from the World Cup final. They were threatening but couldn't crack David Ospina.
It was a stunning end to normal time that left England ragged and reeling.
The round of 16 match against Colombia was tied 1-1 after regulation.
Can Colombia pass the England challenge?
England's extra rest - head coach Gareth Southgate rotated his lineup in his team's final group-stage game - is another factor in its favor.
Expect a narrow England win, with a Harry Kane goal nearly a certainty.
England though, have a tricky round of 16 match against Colombia on Tuesday but then would have winnable games against Sweden or Switzerland in the quarter-finals and Russia, Croatia or Denmark in the semi-finals on their route.
Colombia's players were strangely put out by the decision to pull Carlos Sanchez up for wrestling Kane to the deck, yet Henderson was the only player booked in a lengthy wait that ended with England's captain smashing home. The midfielder has not exactly had a good showing so far at the World Cup, which might force Jose Pekerman's hand.
"If we see it any other way and just think about the pressure, let the situation get to us, we won't play freely".
That would prove the last qualifty chance before the game went to penalties, in which England had not won since 1996.