Real Madrid playmaker Luka Modric then went over in the area but immediately got up and quashed any penalty appeals from his teammates.
© PA Photos
The Bayern Munich frontman tracked down a short Ashley Williams backpass and blocked Price's attempted clearance before sidefooting home.
The lead was doubled soon after the interval when former Arsenal striker Eduardo poked home after Price could only push out a header from a corner.
Price again rescued Wales by denying Eduardo before the visitors had their best opening of the match.
Andy King was left unmarked in the area but the Leicester City midfielder's header went straight at Stipe Pletikosa.
As the game drew to a close, Bale continued to supply the only threat from Wales, twice forcing Pletikosa into saves.