Shazamify allows you to play your Shazams in Spotify, directly from the browser.
Shazamify adds a small Spotify icon to every Shazam track page and allows you to play that track directly on Spotify.
UPDATE 5: I had to publish a new extension as the old one was constantly taken down with no explanation, thanks Google again 😒.
UPDATE 4: Since mid-2017 Spotify blocked unauthenticated API calls, unfortunately, because of that, the user scripts are no longer working :(
UPDATE 3: The Chrome Extension was taken down without any notice from the store. Thanks Google, thanks! I am trying to figure out what I can do about it. In the meantime, you can use the User Script solution.
UPDATE 2: Shazamify, ehm…, Zamify is back online! Enjoy :)
UPDATE: Unfortunately for a matter of copyright with Shazam (even if I work with them) the Chrome Extension was taken down. In the meantime, I’m trying to reupload it to the Chrome Web Store (with the fancy name on Zamify) you can install it as User Script. Shazamify User Script
I wrote also a little compendium on how to install an User Script.