Ospreys coach Sean Holley made three changes to the team that picked up a 19-12 opening win over Connacht, with Andrew Bishop and James Hook added to the backs and Paul James coming in at loosehead prop.
International duo Jonathan Thomas and Tommy Bowe were also included on the bench, the former returning after a seven month lay-off with a groin injury.
Ulster, beaten 43-0 at this venue last term, brought in Clinton Schifcofske and Ed O'Donoghue due to injuries and a fit-again Darren Cave was recalled to midfield.
The Ospreys took the lead in the fourth minute, Hook landing a penalty after Danielli was pinged for a ruck offence.
In summery conditions, Ulster regrouped well and hit back immediately with their first try.
Ian Humphreys set the visitors on the attack, stand-in skipper Chris Henry was also involved before Timoci Nagusa set Dan Tuohy free to gleefully touch down in the right corner.
Humphreys, who missed the conversion, turned creator once again on 10 minutes when he intercepted a pass in midfield from Jonny Vaughton and fed Danielli who finished with aplomb, cantering in behind the posts for a seven-pointer.
The Ospreys looked shellshocked for a time but gradually cranked up their attacking play, which was highlighted by winger Nikki Walker's fine 18th-minute try.
The Welsh region tore out of their half thanks to a brilliant Andrew Bishop break and Mike Phillips also carried well before Walker outpaced his countryman Danielli for the left corner.
Hook's missed conversion was followed by two long range penalty misses by the Ospreys number 10, while Humphreys was able to boost Ulster's advantage to 15-8 with a penalty from closer in after a good run from Nagusa.
The visitors had to cope with the loss of Tuohy through injury, following an attempted tackle on Jerry Collins.
And Ulster had a crushing end to the half. Some miscommunication between Humphreys and referee Alan Lewis saw the former kick the ball into touch expecting the half-time whistle to be blown.
But Lewis insisted there was still time for more and the Ospreys clinically seized the opportunity to close up the gap.
The Ospreys pressed forward, visiting full-back Schifcofske was yellow carded for interfering at a ruck, and from the resulting lineout replacement Duncan Jones was driven over for an unconverted score.
Hook missed the conversion again, leaving it 15-13 to Ulster at half-time, but he redeemed himself on the restart by firing over a penalty.
Narrowly wide with a subsequent place-kick, Humphreys increased his influence on proceedings by beginning the move which led to Ulster's third try.
He linked with Nagusa, who kept the move going with a lovely offload out of the tackle, before a well-timed pass from young centre Ian Whitten gave Danielli the opportunity to dance his way past Collins for his second of the evening.
Humphreys failed to convert and he also missed a late penalty, but Ulster, thanks to huge commitment and spirit from numbers 1 to 22, defended manfully to see out a fully-deserved win.
While understandably disappointed with his own side's display, Sean Holley expressed his admiration afterwards for the way Ulster had gone about their business.
"It was a pretty undercooked performance, and a disappointing one from our point of view. A lot of credit has got to go to Ulster, they made it difficult for us," he said.
"We couldn't get our set piece functioning very well, they fanned well in defence and blitzed hard, and our boys found it difficult to cope with.
"Ulster got in our faces tonight more than they did against the Dragons last week, they were excellent, you can't take that away from them.
"Ian Humphreys was a threat, I thought that their back row was outstanding and Isaac Boss was also a threat. On the night we couldn't really cope with it and that's disappointing."
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|Ulster Rugby Score Card|