The Welsh side took a 24-0 victory over Zebre at home last weekend, while Franco Smith's side beat Dragons 49-0 at Scotstoun.
But in the last meeting between the two clubs in March, Ospreys opened up a 15-0 lead on their way to a 32-31 win in Glasgow.
"It's going to be a difficult match," said Smith, who moves to full-back for tomorrow's game.
"Travelling away from home is always difficult in this league. Ospreys are playing a good brand of rugby, they had a good win against Zebre last week so it's going to be a tough game in tough conditions probably.
"As we've seen in the last couple of weeks, especially last week, Ospreys start pretty well. They scored two early tries and it was the same when we played them at Scotstoun last year.
"We got stung a bit in the first 20 minutes so there's a lot of focus on the first 20 minutes from us, coming out the blocks fast and starting the game from there.
"It comes back to being ready to go from the first whistle and not taking too long to get into the game."