It was a ferocious start from the hosts, but the visitors steadied when Jordan Kahu beat two defenders for the opening try in the fifth minute.
Stand-in Sharks fullback Gerard Beale replied not long after, only for James Roberts to show his speed in racing to a Milford grubber to give Brisbane the halftime lead.
Boyd assisted for Corey Oates soon after the resumption, before Cronulla made a game of it through tries to James Maloney and Ricky Leutele in the space of 10 minutes.
But Milford's effort gave them the breathing space they needed to topple a Sharks side, missing departed grand final heroes Michael Ennis and Ben Barba, as well as injured Valentine Holmes.
Boyd was arguably the Broncos' best, but was aided by strong performances from his starting forwards, all of whom carried the ball for more than 100 metres.
Broncos forward Alex Glenn failed to finish the night after a first-half concussion.
Broncos coach Wayne Bennett admitted it was a scrappy game, but was delighted with the way his team fought off the Sharks' second-half comeback despite losing Glenn at halftime.
"Just our refusal to give in. A player down at halftime there, a lot more pressure on everybody else," Bennett said after the win.
"Our ball control in the second half won us the game. It allowed us to maintain the lead. Cronulla played like a premiership team. That's what premierships do."
Sharks coach Shane Flanagan said his team let themselves down with ill discipline.
"Can't win football games when you turn over the ball and give penalties away. We were 10-5 in errors and 10-5 in penalties. We just gave them too much football," he said.
"We were our own worst enemies. Disappointing from the standards we set ourselves last year so we're really disappointed."
