India's Saina Nehwal and Jwala Gutta and Ashwini Ponnappa won the two matches for their team.
India will play their second and final Group 1D match against South Korea on Wednesday with the winner progressing to the quarter-finals.
In the men's doubles the Indian pair of Manu Attri and B. Sumeeth Reddy went down to Goh V. Shem and Tan Wee Kiong 15-21, 16-21.
World No.2 Saina defeated Tee Jing Yi 24-22, 21-13 in women's singles to level the tie at 1-1.
In the crucial men's singles tie Lee Chong Wei beat World No.4 Kidambi Srikanth 21-16, 21-15 to help Malaysia take a 2-1 lead in the contest.
Jwala Gutta and Ashwini Ponnappa came out with a surprise when they stunned Vivian Kah Mun Hoo and Woon Khe Wei in women's doubles to win 21-18, 19-21, 21-15.
In the mixed doubles match Malaysia sealed the tie with Chan Peng Soon and Goh Liu Ying beating N. Sikki Reddy and Arun Vishnu 21-14, 21-18.
In another match, Group 1C’s Indonesia beat England 3-2 to hand them their second loss of the event after being hammered 4-1 by Denmark on Sunday.