Gareth Southgate's men were taken to extra time after looking like they would win the game 1-0, when Yerry Mina scored with two minutes of normal time remaining.
The centre-half rose highest to head home past Kieran Trippier, who was covering the post, to notch his third goal of the finals, and give Los Cafeteros a chance to sneak through.
Colombia were poor throughout the game, showing none of the football that had landed them a place in the last 16 and instead resorting to overly aggressive play and gamesmanship.
They were seriously hurt by the lack of their talisman James Rodriguez, who had to watch from the stands after failing to recover from a knock.
England had many good performers on the night, but arguably no one better than Everton goalkeeper Pickford, whose save from Mateus Uribe's long-distance effort will very likely be named saved of the tournament.
Frustratingly Mina then struck from the resulting corner, but the Everton star rose to the occasion in the shootout, denying Carlos Bacca and handing the chance to Eric Dier to send England through.
Fans were ecstatic after the game, and there was an outpouring of adulation for Everton's number one:
Jordan Pickford with his wrists of steel.— kopite (@stuartclark1892) 3 July 2018
great save..— Prakhasta (@yprakhasta_) 3 July 2018
I think you deserve to be a man of the match @JPickford1
The renewed David seaman!— Paul B Toovey (@paul2v) 4 July 2018
Outstanding— Wendy Alice Marfleet (@AskJosMum) 3 July 2018
You made us all proud, come on england— Vicky (@vj19842000) 3 July 2018
What a save Gordon banks— ben lucas (@Benlucas03) 4 July 2018
Pickford hasn’t received anywhere near enough credit for this save... pic.twitter.com/i9e2Y33tcA— Warren Grant (@CoachWG1) 4 July 2018