The Welsh side opened the scoring when they spurned an easy penalty and instead opted for a scrum, driving the Sarries pack back over their own line before ex-Australia international Lyons dropped on the ball for a converted score.
The scoring had started on 11 minutes when Banahan had an easy run to the corner after taking Michel Claassens' pass when Alex Tait unwisely went for the interception.
Bradford subsequently turned the screw as Newton flicked a pass to Evans to touch down before scoring himself - after which the soon-to-be retired Vagana missed an easy conversion attempt.