Blues won their first round game with Nottingham comfortably, taking a 38-14 advantage into the second leg last weekend.
Then they were 52-19 victors after the game at Goldington Road, setting up the contest with Pirates. The second leg is back at home on May 7.
Blues scored 11 tries in all over the two opening round legs including Dean Adamson dotting down his 100th for the club.
Cornish Pirates, meanwhile, progressed as one of the two best losers having suffered their first home defeat of the 2021/22 campaign as part of an overall defeat to Doncaster Knights.
Following Saturday’s narrowest of defeats to Coventry at The Butts Park – Ampthill lost 31-22 on the day, and 52-49 on aggregate over the two legs, but are through to the cup quarter finals as the other best loser.
Ampthill will now face the Championship champions, Ealing Trailfinders who received a bye to the Quarter Finals, and will play them over two legs at home and away this Saturday and again on May 7.
Bedford Athletic completed their title winning season in Midlands 1 East with a 55-42 victory at West Bridgford.
Undaunted by a trip to the second place team who were unbeaten in nine matches, the visitors instead extended their own winning sequence to 15 to finish the league season with just one defeat in 24 matches.
Bedford Athletic had dominated their league campaign from start to finish and in dropping only eight points throughout the season were worthy champions.
They complete the season with the Bedfordshire Cup Final at home to Leighton Buzzard on Saturday with a 3pm kick off.
In Midlands 3 East (South) Queens finished their league fixtures on a high with a 22-18 win over Luton. Queens finish the season tenth out of the 12 teams, above Spalding and Daventry.
Having been awarded their game with Thorney, Bedford Swifts finish their league campaign fourth in Midlands 4 East (South).