Sarina Wiegman's side were seemingly set to go into the break a goal down thanks to Leicy Santos's sublime opener, but Lauren Hemp drew the Lionesses level just before half time, and a powerful Alessia Russo strike punched England's ticket to the final four.
With the suspended Lauren James watching on from the naughty step, Ella Toone came into an otherwise unchanged England XI, and the European champions exploded out of the blocks in Sydney.
Hemp and Russo were both thwarted by a sea of Colombia bodies from close range in the eighth minute, before the latter's deft header was kept out comfortably by Catalina Perez.
However, an aggressive Colombia side - who were not afraid to leave a little bit on Wiegman's players - soon began to establish a foothold in the game, despite losing right-back Carolina Arias to injury within the opening 15 minutes.
Nelson Abadia's side would see their endeavours rewarded on the stroke of half time, as the bright Santos sent in an outswinging cross-cum-shot from the right, which beat a stretching Mary Earps and nestled into the far corner of the net.
There were shades of Ronaldinho's goal against England in the 2002 World Cup as Santos's lobbed attempt flew in, but England were awarded six minutes of injury time to try to restore parity, which they did in unorthodox circumstances right at the end of the half.
A loose ball would seemingly be meat and drink for Perez to gather, but the Colombia goalkeeper inexplicably let the ball slip from her grasp, and Hemp was the quickest to react to poke home following an almighty goalmouth scramble.
The Lionesses left the field with smiles on their faces, and the psychological boost from scoring just before the break proved priceless, as England turned the tie on its head 18 minutes into the second half.
Georgia Stanway's through ball for Russo met the legs of a Colombia defender, but the Arsenal forward got lucky with a deflection and raced through to fire home across Perez's goal.
A nightmarish few minutes for the Colombia goalkeeper then saw her replaced by 20-year-old Natalia Giraldo with an apparent injury, but the Powerpuff Girls were not waving the white flag, and Lorena Bedoya forced a strong save from Earps with a stunning long-range strike in the 77th minute.
However, Colombia's subsequent efforts to keep their World Cup dream alive proved futile, as Wiegman's charges set up a tantalising semi-final with co-hosts Australia on Wednesday.