Olly Cracknell, Freddie Steward and Joe Heyes also touched down for Leicester.
Billy Searle kicked four conversions and a penalty to cement Leicester's advantage.
Theo McFarland, Rhys Carre, Juan Martin Gonzalez and Charlie Bracken scored Saracens' tries, with Fergus Burke converting all four.
Steward and Cracknell bagged early tries to put Leicester in command.
And although McFarland's try cut the deficit, Radwan took over with a dashing score from Searle's kick.
Saracens sent on Maro Itoje, the England captain making his first club appearance since October.
Itoje couldn't stem the tide as Leicester delivered the knockout blow in the second half, thanks to another eye-catching Radwan try.