The Blues have never won the Celtic crown but have timed their title charge almost to perfection, extending their unbeaten run to six games to move top the table for the first time this season with just two games remaining.
Mike Phillips and Co proved too much to handle for an injury-hit Dragons side who slumped to their fifth straight league defeat without their star players.
Wales scrum half Phillips stormed over from distance with a typical barnstorming run on 17 minutes before delivering the scoring pass to Rush for a 17-3 half-time lead.
The Dragons hit back early in the second half through flanker Joe Bearman but Tom Shanklin broke clear minutes later and Phillips smashed through to secure the Blues' 15th consecutive league win at the Arms Park, equalling the Magners League record.
Gareth Maule grabbed a late consolation score for the Dragons.