Ramandeep Singh scored both of India's goals and perhaps should have pulled India level with a minute to go, but the other Indian forwards had a mediocre outing.
Lola sealed the first victory for Spain in the tournament by converting a penalty corner five minutes later. The Indians only had themselves to blame as a below-par opening 20 minutes and some sloppy defence ruined their hopes.
Gonzalo Peillat's goal sandwiched in between two efforts from Maico Casella gave the South American side a commanding lead, with Shan Ali's 49th minute strike proving to be little more than a consolation.
India's goals came from Ramandeep Singh (24th, 26th).
With the defeat against Malaysia still fresh in their minds, it remains to be seen how the Indians regroup so quickly.
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Meanwhile, in other quarterfinals of the day, reigning Olympic champions Argentina will play Pakistan, the Netherlands will take on China and hosts England will square off against Canada.
A win will ensure India's place in the fifth-sixth place play-off match scheduled for Sunday. They are also hosts of the 16-team World Cup next year, for which the four semi-finalists in London - Argentina, Malaysia, Netherlands and England - are now confirmed participants.
With such a dismal show, Pakistan got into the quarter finals of the league when Canada which needed a win against Scotland to make it to the quarter finals played a 1-1 draw. The 1-1 result remained until the end of the first half.
A defeat on Saturday will definitely raise question marks over the team's and chief coach Oltmans' progress over the years. While successful circle penetrations were not easy to come by for India, Malaysia surprised them with two goals in the first five minutes of the second quarter that dented India's start.
In the match against India held at Lee Valley Hockey and Tennis Centre, Malaysia took the lead through penalty corner specialist, Muhammad Razie Abdul Rahim in the 19th minute before forward Tengku Ahmad Tajuddin Tengku Abdul Jalil doubled the advantage, a minute later. Malaysia, in contrast, managed seven penalty corners and 12 shots using their speed on the counter-attacks.