Success for Dragons would be their first victory in Llanelli since 2007, but the history of the tie does not concern Harris.
And the South African insists his side has a good chance of causing an upset, if they play to their strengths and do not make needless errors.
"Everyone is positive after a good win against Treviso last week but there are still a lot of work-ons," the prop told the South Wales Argus.
"If we give the Scarlets as much turnover ball as we did Treviso then we will be in trouble so that's the big focus along with discipline.
"There's been a bit of over eagerness and maybe we need to relax a bit more. The guys were out to prove a point and put in a big performance for the crowd so we just need to be more composed and keep hold of the ball.
"The Scarlets have been playing good rugby and have set the benchmark but the tough challenge is good for us as underdogs."
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