Spain skipper Bonastre Berta put them ahead again (30th) but India retaliated and levelled terms just at the stroke of half time with Navneet Kaur scoring in the 34th minute.
The second half belonged to India as they breezed to a 4-2 lead by the 48th minute with goals from Vandana Kataria and Rani, securing a last-four berth for the first time.
This is India’s best performance so far in this tournament, the previous best being ninth in 2001 and 2009.
India head coach Neil Hawgood said: “The success has come from all the big losses as we have been beaten by the top teams in World League Round 3. Now, this experience helps the girls here. The girls were a bit nervous at the beginning but they showed character and continued to work for 70 minutes.”
India skipper Sushila Chanu Pukhrambam said that the team showed spirit.
“Today’s key was the scoring and the team spirit. We decided to win this match and played fast. We are very excited as we have never reached the semifinals before. We would love to qualify for the final,” said Sushila.