England's fourth successive victory in as many games in Pool B gave it the maximum 12 points, three more than Australia, which beat third-placed Spain 2-0.
India was left out of semifinals contention for a ninth consecutive World Cup since it won in 1975, while four-time winner Pakistan was also out of the running after giving South Africa its first win, 4-3.
England's only previous semifinals appearance was in 1986, when it lost the final to Australia.
On Saturday, James Tindall (16th minute), Ashley Jackson (43rd) and Nick Catlin (47th) shot England ahead 3-0 before the lead was cut to one by Gurwinder Singh (54th) and Rajpal Singh (57th).
Australia won its third straight match at Spain's expense, and can qualify for the last four on Monday with a win or draw against Pakistan. Australia hasn't missed the semis since 1978.
“We're close to the semifinals, but still not guaranteed a place,” said Australia coach Ric Charlesworth, who was captain of the only Kookaburras to win the World Cup in 1986.
Luke Doerner's penalty corner conversion in the 20th minute gave Australia the lead and tied Doerner with Taeke Taekema of the Netherlands as leading goal-scorer, with six each.
Glenn Turner then deflected in a square-pass from Robert Hammond in the 60th to dash Spain's hopes of a comeback.
“Scoring 12 goals against South Africa in our last match has given us a big advantage on goal difference,” said Charlesworth, but he was critical of the umpiring.
“I'm very angry with the umpiring. On one occasion, a Spanish player fell himself and the umpire awarded a penalty corner against us,” Charlesworth said. “We also got bad umpiring in the first match.
“It's disappointing and a concern for me. Umpiring is one of the problems with this game and I've been constantly telling my players that we have to overcome it by playing good hockey.
“When it's the World Cup, the umpiring should be good.” Spain coach Dani Martin said his team paid the price for missing good chances.
“It's very clear that if you don't score goals on seven penalty corners, then you cannot win a hockey match,” he said.
South Africa's win over Pakistran was not only its first at this World Cup, but in four World Cups in total. In 17 previous matches, South Africa had drawn six and lost the rest.
Pakistan opened the scoring in the fifth minute through striker Rehan Butt and led 1-0 at halftime. But Gareth Carr equalized in the 38th on a penalty corner before field goals from Ian Haley, Tanie Paton and Marvin Harper gave South Africa a 4-1 lead.
Pakistan pulled back two goals in the last three minutes on penalty corners through Muhammad Imran and Waseem Ahmed.
“I've never seen Pakistan play so badly during my time as a player or coach,” said Shahid Ali Khan, the Pakistan coach and former international.
On Sunday, Germany and the Netherlands play for top spot in Pool A, plus it's South Korea vs. Canada, and New Zealand vs. Argentina.
