Forward Alessia Russo (24) scored the winner for the European champions just after the hour in front of 75,000 in Sydney to end Colombia's run in the tournament.
Earlier in the day, co-hosts Australia beat France 7-6 in a thrilling penalty shootout in Brisbane to reach the last four for the first time in their history.
The semi-final will be in Sydney on Wednesday.
Colombia, playing in their first quarter-final, took the lead against the run of play through a wonderful dipping effort from the edge of the box by Leicy Santos on 44 minutes.
But England struck back deep in first-half stoppage time when Lauren Hemp pounced on a goalkeeping error by a fumbling Catalina Perez, before Russo sealed the quarter-final in the Lionesses' favour with her cool finish.
"I am buzzing, we are keeping the dream alive," said Russo.
"We have had to dig deep from the first game, they have so many talented players who can cause you trouble in a second."
Eyeing up the clash with Australia in front of what will be a hostile crowd, Russo added: "It's exciting, what more do you want?
"I think Colombia had a great fanbase here tonight so we had a taste of it."
Colombia have been one of the best-supported teams at the tournament and their fans dominated at Stadium Australia, their yellow shirts vastly outnumbering England supporters.
Colombia are ranked 25 in the world to England's four and they were clear underdogs, even if they did beat Germany in the group phase.
Sarina Wiegman's England were missing potent attacker Lauren James, banned for two games for stamping on an opponent in the win on penalties over Nigeria in the last 16.
But they made the better start and Colombia suffered an early blow when defender Carolina Arias was forced off after 10 minutes when she was injured during an England attack.
Jeers went up each time the Lionesses had the ball but they seemed to be enjoying themselves and finding pockets of space in front of the Colombian defence with ease.
'Proud' Wiegman
Nelson Abadia's side have a reputation for being physical and they dished out some roughhouse treatment.
The 18-year-old Ana Guzman replaced a tearful Arias and twice she left England players in a heap on the floor, but American referee Ekaterina Koroleva waved away appeals for fouls.
Koroleva was in danger of losing a grip on the game with England putting in some flying challenges of their own in retaliation.
Rachel Daly, one of the England players shaken up by Guzman, twice went close midway through the first half, heading at Perez and then firing over from distance.
Colombia had hardly been seen as an attacking force but they took the lead when Santos expertly looped the ball over goalkeeper Mary Earps, who was caught out by the dip of the ball under her crossbar.
All of the South Americans' substitutes raced from the bench to celebrate with Santos and the rest of the team.
England drew level moments before half-time and it was a goalkeeping mistake, Perez spilling the ball under pressure from Russo and Hemp stabbing into an empty net.
Russo put England in front in the 63rd minute, collecting Georgia Stanway's pass on the turn and firing the ball low under Perez, who was substituted soon afterwards.
Colombia threatened a comeback but England held on fairly comfortably and are just two victories away from adding a first World Cup crown to their European title.
Wiegman praised her team's resilience.
"A very tough challenge, but we didn't expect anything else," she said.
"I thought the first half we played pretty good, but we were too sloppy on the ball. Then they were really engaged in the counter-attacks and we conceded the goal.
"But the second half - I'm so proud of the team. We found a way to score and win the final duels."
She did concede though that she might have to learn more about the historic Australia-England rivalry after fielding multiple questions about the intense hype that will surround the last-four clash.
"I just think it's going to be really big. But now I've had a couple of questions about that, so it's probably going to be bigger than I imagined," Wiegman said, smiling.
"So I'll talk to my players and staff and see what that rivalry means.
"Of course, we've played Australia in April," she added, referring to the 2-0 defeat that was Wiegman's first loss as England manager since being appointed in September 2021.
"So we know them and now we're just really happy that we're through. So tomorrow we start to prepare for the Australia game."
