Thirsk have moved five points clear at the top of the Harrogate Premier League after Saturday's fine 4-1 victory at home to Otley Town Reserves, just seven days after they beat the West Yorkshire outfit on their home patch.
However, Peirse feels Deighton will be a firm test for his team as they look to prolong their fine run of form.
"Hopefully, we'll take the Otley performance into the Deighton game and then I think we'll have no problems but we've got to be at our best," said Peirse.
"I went to watch them against Spa recently and Spa beat them 3-0. But on their day we know they can cause an upset.
"It's a potential banana skin against them so we'll have to be at our best."
Peirse is delighted to have the services of defender Chris Hindmarch for the clash but will miss striker Les Williams through work commitments.
"I've just found out I'll have Chris Hindmarch until after Christmas so that's a great bonus for us," he said.
"Unfortunately, Les is working so he can't play but Chris Etheringham managed to play 20 minutes at the weekend so hopefully he'll be fit enough."
Meanwhile, visiting manager Dan Marshall predicts a humdinger of a contest away from his Barr Field ground.
"It should be a great game," said the Deighton boss.
"We're looking forward to it, especially after the result we got against Sherwood in the cup last weekend.
"We know we can beat anyone in this league, we don't fear anyone and that's shown when we've beaten teams from higher leagues in the cups. Thirsk are a great side, though, and we've the greatest respect for them.
"They are also good at comebacks and they've proved that over the last few seasons.
"They've had to come from goals behind to come back and win games and we'll have to look out for that.
"But we come into the game at full strength.
"I think it's one of the first times this season that I've had a full-strength squad at my disposal so that will be good."
On Saturday a brace from James Robson and Dave Young was enough to put Otley to the sword and move Falcons one step closer to retaining the Premier League title.
However, with Pateley still very much in the chase if they win their game in hand, Thirsk manager Peirse is still staying cautious.
But the boss was understandably happy with Saturday's display, as the Thirsk bandwagon keeps on rolling.
"It was a really good performance," he said.
"We dominated for much of the game and we managed to go in 3-0 up at half-time. They did get one back. It was more a punt from one of their lads really which just managed to creep under the bar.
"But we dominated the game really and we could have scored more. I was really pleased with the performance and hopefully we'll be able to take that into the game tomorrow."