The Azzurri have never beaten England in a Test match, coming closest in 1989 when they drew 15-15 with a side captained by Will Carling in a non-cap international.
Italy stunned France in Rome last year and Parisse wants to deliver another famous scalp to repay the 72,000 who have bought tickets to pack out the Stadio Olimpico on Saturday.
"We're confident for sure," Parisse said.
"I think everyone thinks we can win against England.
"It's going to be very difficult to get a historic result but obviously me and the whole team want this result to repay our supporters and everyone there.
"We know that tomorrow we are under huge pressure and have a huge responsibility.
"A lot of people think that because we're playing at the Olimpico in front of so many people that we must win, but England are one of the strongest teams and it will be very difficult.
"It would be a very important result for us if we win. Beating France at home was a boost for us and the whole of rugby in Italy.
"No one imagined we could do it. Everyone talked about it as a difficult game but no one talked about it as a game we could win.
"It's different this year, everyone believes that we can win, but it won't be easy."
Italy were beaten comprehensively at Twickenham last year but it has been a different story in Rome in recent seasons, with England scraping 23-19 and 17-12 wins on their last two visits.
Parisse will equal the record held jointly by Massimo Giovanelli and Marco Bortolami when he captains Italy for a 37th time tomorrow.
"Nick Mallett gave me this responsibility and I've always tried to do it to my best," Parisse said.
"I don't think much about the record, for me it's just important to have the respect of my team-mates.
"It's a huge honour and I hope to do well in the next few years as captain."
New coach Jacques Brunel, in charge for his first match on Italian soil, has made two changes from last week's defeat by France.
Bortolami replaces Cornelius van Zyl in the second row and centre Gonzalo Canale returns in place of Alberto Sgarbi.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.