Murray split with Australia's John Peers at the end of last year - despite the duo reaching the finals of both Wimbledon and the US Open in 2015 - to team up with the 33-year-old Brazilian.
The unseeded British-Brazilian combination secured two breaks of serve to take the first set but it looked like the match would be heading for a decider when Bopanna and Mergea won the first five points of the second set tie-break.
India's Bopanna and Romania's Mergea even had an opportunity when they went 6-4 ahead, but they lost the following four points as Murray and Soares clinched a straight sets win in 89 minutes.
Murray, who helped Great Britain defeat Belgium in the Davis Cup final two months ago, and Soares reached the semi-finals in Doha in their first event together last week before losing to Spanish duo Feliciano Lopez and Marc Lopez.
For their Sydney triumph, Murray and Soares had tough matches to battle through all the way to the final, and the pair were understandably relieved after claiming the trophy ahead of next week's Australian Open.
Of the fightback during the second set tie-break, Murray told the ATP Tour: "Bruno said at five-love 'let's hang around see what happens'.
"We managed to play a couple of good points, get us back in it. We were a bit unlucky with the net cords to go 6-4 down. But we won eight of the next nine points.
"It's testament to us that we fought hard this week. We came through close battles and we're really excited to win our first title together. There are some big ones next week and we will try as best we can."