Pro-Russian separatists earlier allowed bodies from the Malaysia Airlines crash to be taken to the city of Kharkiv and handed over to international experts.
Western nations say the rebels struck MH17 with a Russian-supplied missile, killing all 298 people on board.
Meanwhile, the main rebel-held city of Donetsk has seen heavy clashes.
Eyewitnesses say there is violence near the city’s airport and the railway station.
The fighting in eastern Ukraine erupted in April and is believed to have claimed more than 1,000 lives.
The UN resolution, proposed by Australia, calls for a “full, thorough and independent international investigation” into the downing of the plane over Grabove on July 17.
It also demands that those responsible “be held to account and that all states co-operate fully with efforts to establish accountability”.
“We owe it to the victims and their families to determine what happened and who was responsible,” Australian Foreign Minister Julie Bishop told the meeting in New York.
All 15 council members, including Russia, voted in favor.
However, Russia’s envoy, Vitaly Churkin, warned that the Security Council should avoid jumping to conclusions about the cause of the crash.
UK’s PM David Cameron earlier said there was strong evidence that pro-Russian separatists shot down the plane with an anti-aircraft system known as Buk.
Russia denied allegations that it had supplied such missiles or “any other weapons” to the rebels.
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