The head coach, whose team have not beaten Pirates in Cornwall since they returned to Penzance from Camborne more than two years ago, knows victory today would be worth much more than four league points.
Bristol can banish any lingering memories of last season's Championship semi-final drubbing by winning this afternoon, while also putting daylight between themselves and sixth-placed Pirates.
And Middleton, who has made no attempts to play down Bristol's record at the Mennaye Field, is demanding an emotional performance.
"Our history at the Mennaye Field isn't great – and that's a fact," he said.
"That is not a deterrent for us, we see it as an opportunity – it's time for us to come of age at the Mennaye and say, 'we will conquer this ground and this will set off a positive chain of events going into 2013'.
"To win at the Mennaye would be more than just four points – it will have a bigger impact on our season. If we win there, I've got every confidence that this team can push on to big things, both in the (British & Irish) cup and in the league.
"That could really set the stall out for what the next five months could hold for us.
"If they get a win against us, they have a chance to kick us out of the top four, so going to Pirates holds a number of things for us.
"It holds the opportunity to establish ourselves in the top four and it provides us with an opportunity for a launchpad for the next five months."
Bristol's last victory over Pirates away from the Memorial Stadium came at Camborne in May 2010, when they thrashed their hosts 60-15.
But recent years have not been so kind to Bristol on their travels to Cornwall, and Middleton knows his players must improve on how they performed in their 26-18 win over Doncaster nine days ago if they are to triumph this afternoon.
"We haven't had a lot of joy down there and we have to show more emotion than we showed against Doncaster," he said.
"We are going to have to add significant amounts to our performance – and we've got the ability, it's probably more around decision-making and the mindset of how we approach the game."
Pirates, who have finished third in the Championship in each of the past two seasons are currently in sixth place, three points adrift of Bristol.
But they have only lost once in their last six league games, while their only home defeat so far this season was inflicted by Newcastle.
"I still think they are a good side and they are hard to beat down there," said Middleton. "Add the fact it's a New Year's Day game and they will have a sold-out, or a nearly sold-out, Mennaye Field.
"When that happens, they become a much more potent side than they may be travelling on the road. Whatever we see with Pirates, add 25-30 per cent for what we're going to face, and the way we performed against Doncaster won't be good enough."
Middleton has made one personnel change and one positional change to the side that beat Doncaster, with Jon Goodridge coming in at full-back and Jack Tovey switching to the wing, in place of George Watkins.
Cornish Pirates: W Davies; T Bedford, T Riley, J Fatialofa, B Mercer; K Hallett, G Cattle (capt); A Paver, R Elloway, B Prescott, D Lyons, D Barry, K Marriott, P Burgess, L McGlone. Reps: R Storer, D Semmens, P Joyce, G Johnson, B Maidment, T Kessell, S Hill.
Bristol: J Goodridge; J Tovey, L Eves, J Gadd, D McIlwaine; A Jarvis, R Tipuna (capt); K Traynor, R Johnston, J Hobson, M Sambucetti, G Townson, A Faosiliva, R Pennycook, M Eadie. Reps: R Lawrence, B Douglas, B Glynn, M Mama, J Grindal, T Roberts, F Otto.