Forward Alessia Russo 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 25th in the world to England’s 4th 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.
Eighteen-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.”
Matildas through on penalties
Earlier in the day co-hosts Australia beat France 7-6 in a thrilling penalty shoot-out to reach the semi-finals for the first time in their history on a day of drama in Brisbane.
Cortnee Vine scored the winning penalty to end a remarkable shoot-out in which each team took 10 spot-kicks, following a quarter-final that ended 0-0 after 120 nerve-shredding minutes.
Vine held her nerve to send the crowd into raptures and keep the Matildas’ dream of winning the World Cup on home soil alive.
Australia goalkeeper Mackenzie Arnold had missed a chance to win the shoot-out when her kick hit the post, but then saved twice from Kenza Dali after the VAR spotted she had both feet off her line the first time.
Vicki Becho missed France’s 10th penalty, and it was left to Vine to take Australia through by beating France’s substitute goalkeeper Solene Durand, who had been sent on especially for the shoot-out.
“I’m so freaking proud about this team. The bravery that they showed tonight, unbelievable,” said Australia coach Tony Gustavsson.
“I think we’ll have maybe tonight to celebrate it and then tomorrow we’ll review it and move on to the next game,” added Arnold, the player of the match.
It was an agonising way for France to go out after a tense encounter watched by a sell-out crowd of 49,461.
Les Bleues had been hoping to get to the semi-finals for just the second time, following their defeat in the last four in 2011, but instead go home.
“We had a whole stadium and a nation against us. We produced an exceptional performance, but that’s football. It was destiny,” French coach Herve Renard told the broadcaster France 2.
“Good luck to Australia. I think we deserved more but that’s how it is.”
Kerr comes off bench
Australia’s victory was achieved despite Sam Kerr again being left on the bench at kick-off. But the talismanic Matildas captain, now fit after a calf injury, came on early in the second half and went on to convert her penalty in the shoot-out.
Gustavsson stuck with the same team that started against Denmark in the last 16, while France brought the fit-again Maelle Lakrar back into their defence.
Lakrar really should have given France an early lead to silence the hostile crowd, but the 23-year-old somehow succeeded in diverting an Eugenie Le Sommer shot over the bar with the goal gaping.
That was a let-off for the hosts, who were then grateful to Arnold for tipping a Le Sommer effort behind and for stopping a stinging Lakrar attempt following a corner.
It looked like the occasion was getting to Australia, but they began to threaten in the final minutes of the first half.
They were desperately unlucky not to go ahead in the 41st minute when French defensive hesitancy allowed Emily van Egmond to tee up Mary Fowler for what seemed like a certain goal, but Elisa De Almeida raced in to produce a miraculous block.
French goalkeeper Pauline Peyraud-Magnin then had to come out to clear in front of Fowler, as it somehow remained goalless at the interval.
Kerr emerged 10 minutes into the second half, replacing Van Egmond to the delight of the crowd, and her introduction provided such a lift that Australia very nearly went ahead moments later.
Hayley Raso tried her luck with a rasping drive from outside the box, but Peyraud-Magnin saved and the Juventus goalkeeper topped that with a brilliant block to deny Fowler from point-blank range on the hour mark.
That appeared to pierce some of Australia’s momentum, and the tension increased as the clock ticked down, making extra time almost an inevitability.
France thought they had the breakthrough 10 minutes into the extra period when Ellie Carpenter turned the ball into her own net, but Australia were rescued when the Chilean referee blew for a foul.
Arnold saved superbly from Becho, before France replaced Peyraud-Magnin with Durand as penalties loomed.
Durand is their penalty-saving specialist and denied both Steph Catley and Clare Hunt in the shoot-out, but it was not enough for France.