Victory opened up a gap over second-placed Celtic after Hearts beat the Scottish champions last week to end a four-game run without a win.
But the Glasgow giants, who face St Mirren in the Scottish League Cup final on Sunday, have two games in hand.
Edinburgh club Hearts, however, have a plus seven advantage on goal difference.
Hearts needed just 66 seconds to take the lead on Saturday with Braga first to react when a powerful Lawrence Shankland shot was parried by Falkirk goalkeeper Scott Bain.
Amid fierce wind and rain, both teams had further chances to score before substitute Kingsley gave Hearts breathing space with a fierce strike from substitute Kingsley in the 77th minute.
Falkirk, aiming to get back into the top six, came close to equalising shortly before half-time when Kyrell Wilson rounded goalkeeper Alexander Schwolow, only for his goal-bound shot to be blocked by the arm of Harry Milne.
The home side appealed for a penalty but were denied a spot-kick when the referee ruled Milne's arm was tucked into his body and in a natural position.
Hearts manager Derek McInnes praised his side's resilience, telling the BBC: "We had to play to the conditions. We had two quality moments for the goals.
"We get off to the perfect start. Good combination play, great strike from Lawrence and Braga following in."
He added: "We did what needed to be done, especially second half. We're just thankful for that second goal. It's a magnificent strike from Stephen.
"A lot of teams would have struggled today. It wasn't pretty. But it's December, it's Scottish football. You've just got to get in get the points, and get out."
