The 18-year-old stunned world No 49 Velavan Senthilkumar in five games at the Isaac Theatre Royal.
The world No 125 needed just over an hour to prevail 11-8, 11-6, 6-11, 2-11, 11-5, staving off a mid-game fightback from his Indian opponent.
It comes 12 months after recording his maiden World Events win at the same tournament.
"It was nice to do it last year, there was a bit more pressure on me this time around. But I enjoy playing on this court, so I'm looking forward to another game on it tomorrow," Dunbar said.
"Over the last year or so I've definitely got better at the mental side of my game. It was good to be able to come through after being 2-0 up and seeing him come back to force a fifth game.
"It's an incredible court and stage here. I'm so happy to play on it whenever I can. It's been great to have lots of my friends here and have some people from my club come down to watch me."
Dunbar was to take on two-time world junior champion Mohamad Zakaria of Egypt in today's second-round match.
It was a tougher day for the New Zealand women, with former world No 3 and 11-time New Zealand champion, Joelle King, and Kaitlyn Watts both beaten in five games.
King is making her return from injury, having last played on tour 10 months ago.
She went down 11-2, 7-11, 8-11, 11-7, 11-8 in 50 minutes to Canadian No 1 Hollie Naughton.
