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
Wales's first chance came through Saturday's two-goal hero Gareth Bale, who cut in from the right and curled a shot just wide of the far post.
Price again reacted quickly to push away Milan Badelj's dipping volley before Mandzukic opened the scoring.
The Bayern Munich man tracked down a short Ashley Williams backpass and blocked Price's attempted clearance before sidefooting home.
The visitors managed to keep the deficit to one thanks to Price, who kept out striker Eduardo on two occasions.