The two teams had ended tied 1-1 after the regulation time and the result was decided through a shootout.
India next play South Africa for a placing in 5th-8th positions.
India took a 1-0 lead with six minutes into the second half when Jaspeet Kaur scored on a penalty stroke. The goal capped a strong first-half performance by the Indians, who dominated much of the action in the first 45 minutes of the game.
The goal woke up the Scottish team, which sprung into action after seeing the 1-0 deficit on the scoreboard.
Scotland peppered the Indian net through the rest of regulation and was finally rewarded with the equalizer with 12 minutes left in the game when Susan McGilveray fired in a goal.
It ended a 20-minute span that saw India constantly fending off a strong Scottish attack. Scotland put on pressure to get the win in the last two minutes, but had to settle for extra time.
In the 15 extra minutes, there were several good chances on both ends of the field, but strong goalkeeping saved the day for both teams and sent the match into a shootout.
In the shootout, India held the 1-0 lead after the first round, but Scotland stormed back again and rattled in three goals to take the 3-1 win on the fourth shot, securing their spot in the semi-final.
