India finished second in group A behind China.
In a must-win match for India, the teams played out a goal-less first half.
Norazlin Sumantri scored for Malaysia within a minute of the resumption of second half but Anupa Barla (52nd minute) and skipper Ritu Rani, who converted a penalty corner in the 65th minute, ensured that India reach the next stage.
India will face the winner of Group B -- either Korea or Japan -- in the semifinal to be played on July 5.
Ten minutes after Malaysia took the lead, India started to dominate the proceedings and in the last 25 minutes hardly spared an inch.
Anupa's strike capped a good pass by vice-captain and fellow forward Poonam Rani, while Ritu Rani successfully converted a penalty corner.
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The Indian team's defenders toiled hard to keep Malaysia at bay.
India scored their third win in four matches. They had beaten Sri Lanka and Singapore in earlier games before losing to China.