Gunneswaran, who is the lone Indian left in the fray, defeated Germany's Yannick Hanfmann 1-6, 6-2, 6-1 in an intense match that lasted for one hour and 22 minutes.
Initially, the World No. 122 had fallen behind as he failed to get into his groove in the first set. However, he adjusted his game in the second and was able to break Hanfmann twice. In the decider, both players took a cautious approach but the Indian was able to hold his nerve and progressed through to the final round of the qualifiers.
He had defeated local wild card Harry Bourchier 6-2, 6-4 in the first round of the qualifiers.
Earlier in the day, Sumit Nagal lost his first qualifying round match against Egypt's Mohamed Safwat. Nagal, ranked 128, lost to World no. 172 Mohamed Safwat 6-7, 2-6 in the match that lasted for almost an hour and a half.
The match was earlier scheduled to be played on Wednesday but had to be rescheduled due to poor air quality caused by raging bushfires.
Earlier, Ramkumar Ramanathan had also crashed out of the tournament after going down to Federico Coria in the qualifiers. India's lone woman contender Ankita Raina had also suffered a 2-6 6-7(2) defeat against Bulgaria's Viktoriya Tomova in the women's qualifiers.
( With inputs from IANS )