The Tigers hit back after 10 minutes play to leave the scores after the blues were caught offside at the ruck.
The Blues however were starting to take control of the game with an aggressive defence and some great work at the line-out and in the contact area.
Both fly halves traded further penalties to leave the score 9-6 to the Blues at the interval.
The second half saw the Blues apply further pressure on the home team and were rewarded with a fine try by wing Harry Robinson after a great first phase play from the backs after 49 minutes.
Griffin kicked a further two penalties to put the Blues further in front.
Blues Head Coach Gethin Watts said, "It was a fantastic result for all the players concerned and keeps the momentum going. We have made a conscious effort this year to expand our playing programme to encompass matches against the best teams in British and Irish rugby, as it is a vital ingredient to a players long term development."