Yep. Spider-Man wins. Which, as an aside, is also why Punisher would similarly beat Batman in a properly written showdown (as opposed to a HtH-only competition where Frank is badly injured from the start). Other than being slightly behind in HtH skills and less capable with laboratory science, he's basically everything the Bat is and more.
Daredevil properly written would also beat Batman in pure HtH. Ditto Elektra: Assassin (and then some!).
The list of who could beat Batman just goes on and on ...
And yeah, Spidey's one of 'em. 😛