Given did brilliantly to keep out a Bednar effort with a one-handed save and his stop to keep out a Giles Barnes header from Somen Tchoyi's cross was even better.
West Brom, who had not won at Goodison Park in their previous 11 attempts, were comfortable victors thanks to goals from Paul Scharner, Chris Brunt, Somen Tchoyi and Youssouf Mulumbu.
Having shocked Lazio with a 2-1 win in Rome in their opening match, Salzburg created another stir as they beat last season's Champions League quarterfinalists thanks to goals in either half from Marc Janko and Somen Tchoyi.