A 73rd-minute Adam Reynolds field goal appeared to have taken the Broncos to victory at Suncorp Stadium on Saturday, before Kini, from 55m out, chipped ahead and snatched the ball from Reece Walsh's grasp to race away in the 77th minute.
Kini then saved a last-gasp try attempt by the Broncos when he knocked the ball dead to secure one of the club's great wins and break a five-game losing streak.
"Special players do special things," Titans coach Josh Hannay said.
"We love that young lad because he might drop a ball early but it doesn't stop him. He keeps going after the contest, and he went after it right to the very end and came up with a special play.
"There's a lot of good things happening at the club, but winning is the most important. It gives the players confidence and everyone belief in what we are doing."
The Titans showed incredible resilience to turn the Broncos away at the death.
Brisbane have now lost five matches in a row and sit in 11th position.
The Broncos were wearing their all-black mental health jersey, the same one they donned against the Titans in round 14 last year when a win kick-started a 10-2 finish to the season and a run to the title.
In a detail of symmetry, they had a 5-7 start to the season last year before the Titans clash, exactly the same beginning they had made to this season. History did not repeat itself.
"I can't fault the effort the players are putting in. Last week we weren't where we needed to be, but this week they had a red hot crack," Broncos coach Michael Maguire said.
"We obviously want to turn up and win, that's why we're here. I've got a club that has an expectation around that, but at the moment we're just not able to dig those out."
Ezra Mam, on the extended bench for Queensland in the State of Origin series opener, has been demoted to the Brisbane bench by Maguire for poor form, but entered the fray in the 15th minute when his replacement Tom Duffy suffered a category-two head knock.
The dazzling five-eighth made an immediate impact with four tackle busts, but was replaced after a 15-minute stint when Duffy came back on.
Mam split the defence down the left and centre Kotoni Staggs scored in the right corner to make it 12-0 after Brendan Piakura scored the opener.
Titans super sub Kurtis Morrin, one of their best this season, had the presence of mind and the commitment to win the race after Broncos forward Jack Gosiewski dropped the ball near his own tryline.
Gold Coast winger Phil Sami busted through a feeble attempt at tackle by Ben Hunt and ran straight around Walsh, who was suffering from a cork, with ease in a sensational 70m run to the line as the Broncos took a 12-10 lead into the break.
Brilliant play by Klese Haas and AJ Brimson sent five-eighth Jayden Campbell in under the sticks and the Titans had the lead after 50 minutes.
Campbell zig-zagged his way to his second with individual brilliance, but a crucial Haas error gifted the Broncos the ball and Duffy put Jesse Arthars over out wide.
Mam came on for Duffy again in the 61st minute, but it was Piakura who came up with a stunning ball for Grant Anderson to level
Reynolds stepped up, before Kini came up with a play for the ages to win it.
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