Llanelli have been drawn to play top seeds Bedford Blues in the quarter-final on Saturday 6 April.
Bedford finished 19 points clear of their nearest rivals Stirling at the top of Pool 2 after going through the pool stages without dropping a single point.
Bottom seeds Llanelli got through at the expense of Moseley on points difference. Llanelli managed to hold Bedford to a 25-all draw on their last visit to Goldington Road in the B&I Cup on December 17, 2011.
Bedford, who lost out to Bristol in the 2011 B&I Cup final, are searching for their first silverware since lifting the Powergen Shield at Twickenham in 2005.
Quarter Final Draw, April 5-7
Bedford Blues v Llanelli - Saturday 6 April, KO 3pm
Newcaslte Falcons v Nottingham Rugby - Friday 5 April, KO 8pm
Cornish Pirates v Munster - Sunday April 7, KO 3pm
Bristol Rugby v Leinster 'A'- Sunday April 7, KO 3pm