First off, it should have been 2 minutes on Eakin, though I don't think Stastny was remotely blameless here. He clearly changed an already falling players trajectory with force. He put his leg behind Pav's and then shoved him down. It's certainly an unusual hit, but an incredibly dangerous one. The ref's have the discretion to call a major based on force/effect and that's what they did (but on the wrong player). I also think they likely judged it similar to a hit to the head incident where even if it wasn't done on purpose, it's still zero tolerance (like high sticking).
So I voted no, because it was on the wrong player, but as a 5 minute major is judged based on somewhat vague standards, it's hard to say the rules are clear on this. The ref's saw what they saw, and they are given direction from the DOPS about how to call stuff we are not privy too. Regardless, the Sharks have lost many, many, many playoff games because of extremely questionable calls, it happens, you can't let one bad call sink you. In this case, Vegas had 3 elimination games to close the Sharks out and failed to do so. They put themselves into a position where one bad call at the wrong time might end their season, and then they allowed that to happen. So, essentially, I probably would have called a double minor, but it's irrelevant because game 6 and 7 never should have happened in the first place if Vegas had their shit together.
Also, this series created a ton of animosity on the ice, and the result of that ended up being a furious Sharks team having the emotional edge at the most important moment of the series. If you are going to play with fire, you might get burned.