Not even the returning Brian O'Driscoll was enough to inspire the Irish outfit who fell short in the closing stages despite Ian Madigan's try and 11 points from Fergus McFadden's boot putting them 16-6 up at the interval.
George Stowers' try launched Ospreys' comeback before Dan Biggar completed his 13-point haul with the match-winning conversion, leaving Tandy beaming with pride.
"That performance speaks volumes about the spirit we've got at the Ospreys," said Tandy.
"I always felt we could get the win, I never thought we were out of it.
"I didn't think that the half-time scoreline really reflected the game. We were well and truly in the game but they got a fortunate try that just allowed them to get a little bit in front of us.
"We worked hard, stuck at it, and got our reward in the end.
"We stayed patient and didn't panic, despite the clock running down, defended well and up popped Richard Hibbard to score.
"Dan Biggar kept his cool to send over a great winning conversion but the way we dealt with the last couple of minutes to keep them out was just as pleasing."
"We stuck to our game plan, remembered the things we worked on in the week and it meant we managed to do something not many people manage to do, and that's win in Leinster."
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