Tandy’s men took the lead at Ravenhill thanks to a Joe Bearman try, which Dan Biggar converted.
But Biggar was sent to the sin-bin in the dying moments of the half and Ulster pounced either side of the interval with a penalty try and a Paddy Wallace touchdown.
The Ospreys appeared dead and buried but grabbed an Eli Walker try with two minutes to go to hand his side a glimmer of hope. The teenage wing then came agonisingly close to snatching an injury-time victory but the Welsh region instead settled for just a losing bonus-point.
Ulster laid siege to the Ospreys early on but were unable to capitalise on their early dominance with Ruan Pienaar firing a long-range penalty wide.
Matters were made worse for the hosts when they lost Pedrie Wannenburg to the sin-bin, after the former Springbok foolishly tripped Ospreys scrum-half Kahn Fotuali’i.
The Welsh region kicked to the corner and instantly benefitted from their numerical advantage with Bearman powering through Nevin Spence, following strong carries from Biggar and Eli Walker.
Biggar slotted the extras to hand the Ospreys an unlikely 7-0 lead.
Pienaar hit-back for the hosts on the half-hour mark but failed to cut the deficit further three minutes later.
But Ulster went into the interval with the lead following a last-gasp try. They went through several phases and were awarded a controversial penalty-try after Biggar raced out of the blocks and failed to intercept. Referee Neil Hennessey adjudged that it was a deliberate knock on and Biggar was also shown yellow.
Ulster took further advantage of Biggar’s absence with their second try on 48 minutes. Following a relentless onslaught Pienaar released Whitten, who put Wallace over for the for the score that made it 12-points while the Ospreys fly-half was in the bin.
The Irish province continued to dominate and it was only the heroic defence of Fotuali’i saved another certain try.
Ulster continued to turn the screw as the Ospreys clung to their slim hopes of snatching a victory. But Tandy’s charges enjoyed a bright spell in the closing stages and Walker produced a moment of brilliance on 78 minutes to hand the Ospreys a lifeline.
Biggar converted and Ashley Beck and Hanno Dirksen launched a counter-attack, which almost snatched a dramatic victory. The ball was recycled but Walker was unable to collect Matthew Morgan’s cross-kick and the Ospreys left Northern Ireland with just the losing bonus-point.
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