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, SomenTchoyi and Youssouf Mulumbu.