In the movie, sharks attack people.
Sometimes the people do inherently dangerous things like run from secure location to secure location, try to rescue a friend in danger, etc. These moments are inherently tense and dangerous, these are the times when failure brings death, lost health levels, and pain. This is where all of the normal rules and mechanics from whatever rpg you're playing come in.
Between these moments of inherent danger and risk though... the people do other stuff. Boring stuff. Safe stuff. Sometimes they deliver flat exposition, sometimes they mend wounds, sometimes they fortify their position, sometimes they get to know each other, etc.
The trick is, that each 'safe action', each passing minute without a death or dismemberment, only increases the feeling that another mother fucking shark is about to get a tasty human snack. Substitute sharks for zombies and you have the rhythm of every zombie movie ever made. The longer the heroes avoid doing anything dangerous, the higher the chance the danger will come to them.
The well-versed among you are thinking this sounds a lot like the pacing mechanic in Shotgun Diaries. Well, you're right. And wrong. Shotgun Diaries increases the zombie clock after every 10 minutes of real time. In my opinion, it fails.
I propose increasing opposition after every 'safe action', that is after every action that brings no inherent danger. The PCs want to chat for 30min of quality roleplay? Awesome! Don't interrupt that shit for anything. Don't bring in the zombies when the PCs are at each other's throats and bringing their own danger. Just sit back and enjoy the mayhem! On the other hand, when the PCs fortify their location, investigate the outbreak, heal their wounds, and otherwise avoid the danger outside. A few more zombies gather on the outskirts.
If you want to raise tension in a zombie or slasher style horror game, use this...
Every time a player calls for a dice roll that doesn't bring or risk something dangerous, increase the opposition. In WoD terms, add an extra die to the next enemy attack. In D20 terms, add a +2 bonus to the next baddie.
If your zombies roll 2 dice to attack (or has a +4 bonus to hit), three safe actions between attacks will mean the next zombie rolls 5 dice (or has a +10 bonus). Hell, three safe actions could just as easily allow you to introduce a brand new threat (like a gas leak) at 3 dice!
That's it! Easy enough right?