The Warriors picked up a playoff victory thanks to Klay Thompson's 22 points and a standout rebounding performance from David Lee, who grabbed 20 points and 13 rebounds.
In Indiana, the Atlanta Hawks notched a surprise victory against the top-seeded Indiana Pacers with a 101-93 win at the Bankers Life Fieldhouse.
The Hawks were helped by Jeff Teague's playoff career-high 28 points, while Paul Millsap added 25 to spark eighth-seeded Atlanta to the win.
During the five previous post-season playoff segments where the two teams have met, the Game One winner has gone on to win the series.
The Oklahoma City Thunder were the only home side to secure a win on the opening day of the playoffs, as they rose victorious over the Memphis Grizzlies with a 100-86 win at the Chesapeake Energy Arena.
The hosts were thankful for the game-winning performances of Kevin Durant and Russell Westbrook, who scored 33 and 23 points respectively to combine for a total of 56 points.
Finally, the Brooklyn Nets continued their good form by grabbing a 94-87 win over the Toronto Raptors, as Paul Pierce scored nine of his 15 points in the final quarter to push the Nets over the line.
Results in full: Brooklyn Nets 94-87 Toronto Raptors, Golden State Warriors 109-105 Los Angeles Clippers, Atlanta Hawks 101-93 Indiana Pacers, Oklahoma City Thunder 100-86 Memphis Grizzlies