The Olympic champion jumped 8.10m with his fourth attempt of six - as in London, Australia's Mitchell Watt had to settle for second place.
Watt leapt 8.01m, with fellow Australian Fabrice Lapierre third in a close-fought competition with 7.99m.
"Every competitor always wants to win. Mitch is a friend of mine, so it is not like a bad competition ever," said Rutherford.
"Ultimately, he wants to beat me and I want to beat him but we are always still mates.
Rutherford, who won gold in London with a jump of 8.31m, added: "An 8.10m isn't anything massively special but we are in the early part of the year, and waking up this morning I didn't expect to be able to jump that well so early."
Australian champion Josh Ross ran 10.25 to win a 100m race that was supposed to feature Jamaican Asafa Powell, who pulled out with a hamstring injury. Wallace Spearmon won the 200m in a sedate 20.79.