![[ image: width=150]](/olmedia/50000/images/_50312_stransky.jpg)
![image: [ Michael Lynagh kicks the winning penalty ]](/olmedia/50000/images/_50312_lynaghtop.jpg)
The Londoners' fly-half Michael Lynagh kicked a penalty in the final seconds to earn his side a place in the quarter-finals.
Lynagh's opposite number Joel Stransky scored all Leicester's points. He put the visitors 13-3 ahead early in the second half, racing 30 metres down the touchline for a try which he converted.
Saracens' Australian wing Ryan Constable replied with a try, before Lynagh kicked the deciding penalty.
The game featured 23 internationals and gave Saracens revenge for their one-point defeat by Leicester in a league match last month - their only Premiership setback this season.
Bath were knocked out 29-17 after extra time by Richmond - the only side to win away in Saturday's fifth round matches.
It is a blow for Bath ahead of next weekend's European Cup final against French club Brive.
England international Mike Catt kept Bath in the game with two late penalties - the scores were tied at 14-14 at the end of normal time.
The visitors dominated the scoring in the additional period, including a fine try from winger Dominic Chapman, who is being courted by England and Ireland.
Three other sides made it to the quarter finals - West Hartlepool overwhelmed Rugby 42-11, Northampton beat Gloucester 30-11 and London Irish knocked out Rotherham 27-14.
The final three fifth round matches take place on Sunday: Sale v Newbury, Wasps v Fylde and Worcester v Newcastle.
In Allied Dunbar Premiership Two, Orrell won 30-21 at Coventry, while London Scottish beat their visitors Exeter 22-10.
Swalec Cup fifth round results
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Premiership trio sail into cup quarter-finals