In a contest marked by excessive safety play, the pair was eventually separated in the seventh frame when Mehta came up with two solid breaks of 38 and 33 to close the match.
In the semi-finals, Mehta will take on World No.5 Stephen Maguire from Scotland who put out England's Michael White 4-3, while Ding Junhui of China knocked out World No.1 Neil Robertson from Australia 4-2 to set up a clash with Robbie Williams, an easy 4-0 winner over Anthony McGill.
The 27-year old Mehta, ranked two spots below Advani at 72, kept his cool under intense pressure as the match swung one way and the other as the players traded frames to keep the outcome in suspense.
Eventually, it was 28-year old Advani who gifted away a red while playing a safety shot and Mehta pounced on the opening to win the match. There were just two half-century breaks, 51 and 55 by Mehta in the third frame that lasted 63 minutes and fifth.
World No.4 Junhui extended his domination over Robertson whom he had beaten in the final of the Shanghai Masters recently. In a rip-roaring match, the Chinese ace went 2-0 up on breaks of 72 and 52, but Robertson hit back through runs of 86 and 104 to level at 2-2 only to see Junhui take the next two with efforts of 85 and 91.
White's two century breaks of 133 and 125 could not stop Maguire from winning as the Scot was more consistent with runs of 90, 77 and 73 marking his progress.
Advani and Mehta had earlier survived nail-biting moments while getting past Stuart Bingham 4-3 and Mark Williams 4-2, respectively, providing plenty of thrills to the spectators.
Advani saw off World No.12 Bingham whose two century breaks of 117 and 119 in the second and sixth frames went in vain as the Englishman virtually gifted the seventh by missing a red and leaving it at the mouth of the top right pocket.
Advani, who had two breaks of 53 in the first and fourth, went on to craft an 86 to clinch the match and was gracious enough to admit that he was let off the hook.
"When he was on that run in the last frame, I thought he could take the frame, but I was pleasantly surprised when he missed the red.
"I told myself to play one shot at a time, one ball at a time. The 86 was a very standard break in snooker terms as the reds were all spread. There was nothing special about the break," said Advani.
For Mehta, it was about holding his nerve against the 38-year old Welshman, a World champion in 2000 and 2003, but currently ranked 18th and whose potting ability is second to none.
The decisive moment came in the sixth frame when Williams could not capitalize after Mehta missed a straightforward black after taking the 14th red.
Though the Welshman cleared to blue, but left the black blocking the left top pocket, and the colour proved critical to a bout of safety play by both with Mehta leading by 17 points and 18 on the table.
Mehta sank the blue while Williams played safe on the pink but it knocked the black in for a seven-away thus ending the match.
"These are the situations we come across a lot of time, but I held my nerve. I was shocked when the black didn't drop, and left hanging in the jaw. Yes, it could have become 3-3 instead of 4-2, but I was prepared for the seventh frame, just like in the case of my match with Ebdon," said Mehta who had beaten 2002 World champion Peter Ebdon 4-3 in the previous round.
Quarter-finals: Aditya Mehta (IND) bt Pankaj Advani (IND) 4-3 (29-70, 00-70, 68-82, 58-43, 65-24, 40-65, 72-00); Ding Junhui (CHN) bt Neil Robertson (AUS) 4-2 (96-04, 76-52, 00-86, 00-104, 85-10, 91-00); Robbie Williams (ENG) bt Anthony McGill (SCO) 4-0 (79-00, 70-54, 107-00, 75-26); Stephen Maguire (SCO) bt Michael White (ENG) 4-3 (29-60, 90-22, 00-133, 00-125, 78-00, 73-23, 52-47).
Round of 16: Advani bt Stuart Bingham (ENG) 4-3 (99-26, 01-117, 80-15, 69-16, 11-72, 08-119, 86-30); Mehta bt Mark Williams (WAL) 4-2 (34-65, 79-21, 85-00, 45-74, 63-49, 70-41); Robertson bt Liang Wenbo (CHN) 4-2 (96-39, 61-42, 10-68, 32-65, 87-00, 100-00); Maguire bt Mark Davis (ENG) 4-2 (68-70, 70-00, 00-96, 70-45, 93-16, 69-45); White bt Gary Wilson (ENG) 4-3 (78-49, 00-84, 133-00, 59-43, 25-73, 89-00); Robbie Williams bt Mike Dunn (ENG) 4-0 (57-49, 134-00, 67-05, 63-55); McGill bt Joe Perry (ENG) 4-2 (00-80, 72-52, 77-06, 30-71, 109-22, 138-0); Junhui (CHN) bt John Higgins (SCO) 4-2 (27-84, 62-21, 62-25, 109-00, 00-94, 77-00).
(Anand Philar can be contacted at firstname.lastname@example.org)
--IANS (Posted on 18-10-2013)