Rea, 29, from Northern Ireland, swapped the lead with Ducati rider Davies on the final lap in Phillip Island before edging the verdict by .063 of a second.
Dutchman Michael van der Mark was a further .43 seconds back in third while Huddersfield's Tom Sykes took fifth.
The second race in Phillip Island will take place on Sunday.
This year's World Superbike series has a new format with race one at the meetings taking place on Saturday afternoons as opposed to Sunday mornings.
Race two will continue to be staged on Sunday afternoons.
In Saturday's opener, Davies, 29, produced a tremendous charge from ninth on the grid to challenge an early lead group which also included Sylvain Guintoli and Alex Lowes.
Englishman Sykes led at one stage before dropping back after being passed by Rea.
By the start of the final lap, Davies was Rea's closest challenger and the Welshman took the lead as the riders approached the final corner before the defending champion produced a daring move on the outside to snatch victory.
After being prominent for much of the race on his World Superbike debut, 2006 MotoGP champion Nicky Hayden has to settle for ninth place.
Rea is aiming to emulate the achievement of Carl Fogarty, who successfully defended his title twice in the 1990s.
The Northern Irishman won 14 of the 26 races last year and was on the podium 23 times.
Jonathan Rea began the defence of his World Superbike title with a thrilling victory over Welshman Chaz Davies in Saturday's season opener in Australia.