The Dragons failed to come out of the blocks in the first-half and were put under immense pressure by Exeter’s giant pack and experienced half-backs.
Argentinian fly-half Igancio Mieres landed four first-half penalties as the pressure told to finish the half with a 12-0 lead at the interval.
But whatever Darren Edwards said in the changing rooms appeared to do the trick and the Men of Gwent returned with far more intensity . They were rewarded with two Stefan Jones penalties but it was not enough as the Chiefs turned the screw and Mieres finished the job, denying the Dragons a losing bonus-point in the process.
The victory sees Rob Baxter’s men surge to the top of Pool Four ahead of next Sunday’s clash at Rodney Parade while the Dragons drop to third – but just a point in arrears.
Mieres got the Chiefs on the scoreboard with a well-struck penalty on three minutes to take a 3-0 lead.
He doubled the hosts advantage on 10 minutes after the Chiefs’ pack exerted their power at the set-piece and added a third penalty on 23 minutes to bring the scores to 9-0 as the Dragons were again penalised at scrum-time.
Mieres slotted his fourth penalty on 28 minutes after Bedford failed to deal with a high-ball. The Dragons were dealt a further blow on 34 minutes when the rookie scrum-half was shown yellow after referee Carlo Damasco lost patience at the breakdown.
But Mieres was uncharacteristically off-target and the Dragons weathered a late storm to go into the interval trailing 12-0.
The Welsh region returned for the second-half with far more commitment. Jones was off-target with a penalty attempt on 42 minutes but made amends less than 10 minutes later to bring the scores to 12-3.
And the Dragons comeback continued as Jones added a second penalty on 58 minutes. But Exeter quickly responded and twice went to the corner before Mieres settled for his fifth penalty to put the losing bonus-point out of range.
Mieres then slotted a sixth with the final kick of the game to put the result out of doubt
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