Superb first-half strikes from Lee Connelly and Elliot Embleton (pictured above) were enough to secure top spot in Group B and a place in the last eight for the 2016/17 finalists.
The result left Leicester second on four points, ahead of Hertha Berlin and Legia Warsaw.
They must now wait to learn whether they will progress as one of the two best runners-up. They are the second-placed side with the best record but that could change with three groups yet to finish.
Sunderland: 28 Jan v Arsenal (H) PL2
Leicester: 29 Jan v Man City (H) PL2