With just one round of the regular season to play, the 'Canes lead the table by a point from the Auckland Blues who meet misfiring defending champions Canterbury Crusaders on Saturday.
The ACT Brumbies consolidated their place in third with a 53-17 thrashing of the Melbourne Rebels in Canberra to leave them five points clear of the Chiefs and two behind the Blues.
In front of a sell-out crowd in Hamilton, the Hurricanes raced to a 14-0 lead at the break despite hooker Raymond Tuputupu being sent off in the eighth minute for high contact.
But in a thrilling second-half, the Chiefs rallied to level at 17-17 before fly-half Cameron sealed the visitors' win with a kick from more than 40 metres with a minute left.
"It's huge to get a win on the road, especially at this stage of the season with home finals at stake," said Cameron, who scored 10 points.
"We were happy with how we were going at half-time, moving the ball well. I guess we just had to ride the momentum in the second half, be calm and stay in it."
The Hurricanes scored the first try through prop Xavier Numia and Jordie Barrett added a second to build their half-time advantage.
But the Chiefs' Emoni Narawa and Wallace Sititi crossed in the second half, while Damian McKenzie added two conversions and a penalty to set up the grandstand finish.
In Canberra, a rampant Brumbies ran in seven tries against the Rebels, with Noah Lolesio converting six of them to maintain their unbeaten run at home this season.
Tom Wright (two), Jahrome Brown, Nick Frost, Billy Pollard, Rhys Van Nek and Luke Reimer all crossed for the home side, while Filipo Daugunu and Angelo Smith scored for the Rebels.
