He will meet teammate Sourav Kothari in the last four.
The other semifinal will pit Akshay Kumar (Uttar Pradesh) against former IBSF world 6-Red Championship runner-up Kamal Chawla.
Multiple times world champion Advani raised his level of play after sharing the first four frames with Gulati.
Up 4-2, Advani faced some resistance as his rival came up with some good safety play. He held firm and took the seventh frame to advance.
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"Im feeling very happy, words can't explain how happy I am. I played well and I'm looking forward to play the same way tomorrow in the semis", Akshay said after the win.
In the other quarterfinals, Chawla of RSPB defeated Ishpreet Singh of Maharashtra 5-3 and Kothari beat Varun Madan of Delhi 5-3.
By entering the semifinals, Advani, Kothari, Akshay Kumar and Chawla have qualified to represent India in the Asian 6-Red snooker championship to be held next year.
In the pre-quarters, Pankaj defeated Pushpender Singh 5-1, with a phenomenal break of 74 in the match. Tamil Nadus G Prabhu and Vijay Nichani lost out to Akshay Kumar and Sourav Kothari respectively.
Pre-quarters: Akshay Kumar bt G. Prabhu 5-3 (35-1, 14-43, 7-44, 68-0, 9-44, 52-16, 34-33, 46-17); R Girish bt Avinash 5-1 (51 (43)-6, 42-4, 35-22, 9-48, 48-3, 49-8); Kamal Chawla bt Vinayak Agarwal 5-1 (26-54, 72 (42)-0, 42-24, 37-20, 34-20, 53 (53)-0); Ishpreet Singh Chadha bt Malkeet Singh 5-3 (35-5, 17-34, 18-32, 28-20, 47-6, 36-6, 14-32, 42-4); Varun Madan bt I Have Manudev 5-2 (40-16, 23-31, 45-8, 46-21, 29-36, 38-10, 44-22).