Vault does best with big handsizes, and Caravan is just about the cheapest non-terminal route to big hands. Of course, Laboratory, Village/Council Room, and Tactician (among others) are also great ways to increase your hand size, but they’re much more expensive and therefore less viable in poor decks. In order for this to work, you have to really spam the Caravans, which is not too difficult since it’s relatively easy for a deck to consistently hit $4.
Haven can substitute for the Caravan, but it’s less readily spammable than Caravan because each Haven you play lowers your hand size. It can, however, move your Vault from a small hand to a bigger one.
I won this game for two reasons: first, my Caravans were more effective than his Caravans, because drawing even a Curse meant another +$1 for the Vault; two, his Worker’s Village/Rabble combo was slow in the beginning with Curses and slow at the end with Victory cards, while Vault can keep on churning even when the deck is clogged with Curses and Victory cards.