Though most people will disagree with me, I think Sasuke can pull out a win, but only if he remains calm and has his Hebi personality. Luckily, he will remain calm, unless Minato says something negative about Itachi to get him flustered. I'll start by saying how Sasuke counters Minato. Firstly, if Sasuke gets tagged, he is dead, but with MS Sasuke's readiness to use Susano'o, he won't get touched, which also makes Contract Seal useless. Not that Sasuke will need summons. If Minato uses Food Cart Destroyer, Sasuke will tank it with Susano'o then proceed to burn Gamabunta down or control him with Sharingan and use him against Minato. Minato's shunshin shouldn't be much of a problem for Sasuke, considering his own speed and the fact that he has sharingan. Rasengan, Kunai slashes, and taijutsu all get tanked, and may end up costing Minato his body parts, if Sasuke opts to set his Susano'o ablaze.
Since Minato tends to litter the battlefield with kunai, considering the location is under the bridge, they will sink, but I'll ignore that. When the land, after Sasuke tries Amaterasu and fails, he will find out why Minato spread out the Kunai, and opt to burn them all, which should be easy considering he will know where they all are. Space Time Barrier will be a problem, as it will render all of Sasuke's projectiles useless, but those are not needed. After he burns all of the kunai and corners Minato, one of two things will happen. Minato will warp away to a safe house, or use Shiki Fuujin to end it in a draw. Sasuke can get around this though, by putting Minato in genjutsu.
Out of 10 times I say Sasuke wins 2 times, as he isn't completely hopeless against Minato, Minato wins 2-4 times, with the remainders being draws, due to them being incapable of killing the other, and Minato warping away or using Shiki Fuujin when all hope is lost.