Lima struck 10 minutes before half-time to open the scoring but the hosts had to wait until the final minute for Matheus to make sure of the points after they caught Partizan on the break.
GEAR:Champions League shirts here. Free worldwide delivery on orders over £40
Braga lost their first two group games, conceding nine goals and failing to score, but coach Domingos Paciencia believes the win can help them recover enough to qualify for the knockout stage or at least secure third place and a Europa League spot.
Braga are six points adrift of leaders Arsenal but only three behind second-placed Shakhtar Donetsk who were thrashed 5-1 in London. Partizan are bottom without a point.
LIVE:Minute-by-minute coverage as it happened
"We're going to put up a fight, try for the maximum points we can, knowing second place is within reach and third place quite possible. That's how we have to think," Paciencia said.
"It was an important game, against a direct opponent at this stage, and we had to take risks. We were more efficient, and so won justly," he added.
Lima opened the scoring with the first real chance after 35 minutes, firing a thunderous 30-metre free-kick into the top corner past keeper Vladimir Stojkovic who got a slight touch.
MORE CHANCES
"I think the result flatters Braga a bit because we created more chances and they scored with their first shot on target so we are really disappointed with the result," Partizan coach Aleksandar Stanojevic told Serbian television.
Braga came close to scoring again but Stojkovic twice denied them, stretching to reach a Paulao header in the 48th and then coming out bravely to block Matheus' shot after 76 minutes.
However, the Portuguese side finally got a second goal in the last minute when Matheus scored with a simple tap-in after a counter-attack led by Alan and substitute Luis Aguiar.
Apart from Almami Moreira's aggression in midfield, Partizan carried little bite in the early exchanges and their only attempts were long distance shots from forwards Marko Scepovic and Cleo that Braga keeper Filipe held without trouble.
But the Serbian champions almost equalised two minutes after falling behind when Milan Smiljanic sent a fine pass into the box for Aleksandar Lazevski but the left back volleyed wide.
With Braga threatening more in the second half, Stojkovic, targeted by fans of Partizan's rivals Red Star Belgrade at last week's abandoned Euro 2012 qualifier in Italy, was called on several times but could not prevent Matheus sealing the points.
The two sides meet again in Serbia on November 3.
Stanojevic added: "It will be even more difficult for us in Belgrade because they (Braga) are a good counter-attacking team and throwing men forward in front of our own fans means we will have to give them room to operate on the break."
