Kershaw, who signed a seven-year, $215 million contract in January, allowed one run and five hits in 62⁄3 innings. Van Slyke hit a two-run homer and also doubled.
The first pitch was delayed because of rain for 14 minutes. By then, the long trip Down Under had taken even longer for some Arizona players.
A team bus had a flat tire, and the Diamondbacks said "a handful" of players decided to walk the last half-mile to the stadium instead of waiting for a replacement bus.
Kershaw was impressive while making his fourth consecutive opening-day start. He struck out seven, walked one and was pulled by manager Don Mattingly after throwing his 102nd pitch.
Quite a turnaround from spring training, when the two-time NL Cy Young winner went 0-3 with a 9.20 ERA in four starts.
"Sometimes you just need the adrenaline of a regular-season game, and I just kind of feel relieved to get this one under my belt," he said.
"It's always good to get results, obviously," he said. "This one counted."
Around the horn
Braves • Julio Teheran, who was 14-8 with a 3.20 ERA last year as a rookie, will get the opening day start for Atlanta. Manager Fredi Gonzalez told Teheran on Saturday he'll start on March 31 in Milwaukee. The Braves didn't have much choice after a string of injuries this spring. Kris Medlen and Brandon Beachy are sidelined because of elbow ligament transplant surgery. Ervin Santana, who signed late as a free agent, and Mike Minor (shoulder) won't be ready to join the rotation until mid-April.
The Braves will go with three other starters the first two weeks of the season Alex Wood, Freddy Garcia and rookie David Hale.
Teheran has a 1.42 ERA in five spring starts. He has 17 strikeouts and three walks while holding opponents to a .194 average.
Brewers • Ron Roenicke has a contract to manage Milwaukee through next year after the club exercised its option for 2015. General manager Doug Melvin says he is confident in Roenicke after the skipper's leadership through an injury-filled and sometimes turbulent season last year. Roenicke, entering his fourth year in Milwaukee, has a record of 253-233.