The first daytime direct train leaves Wien (Vienna) at 06:30 and arrives at Venezia Santa Lucia at 13:26. The next one leaves at 12:57 and arrives at 21:20 (longer because of more stops).
If you have a Eurail pass that includes the appropriate countries, it would be good on those trains, but you would have to pay a reservation fee.
The SparSchiene fare is €29 for the direct day trains. SparSchiene fares for the direct night train vary according to the type of sleeping accommodations you choose--and they may compare favorably to the supplement you would have to pay for sleeping accommodations if you have a railpass. Unless you read German, booking by phone would be easier than booking online. Book ASAP (up to three months in advance) because SparSchiene tickets are limited. Dial your country's international access code + 43 (country code for Austria) + 5-1717.