Boss Brendan Rodgers challenged Leicester to finish the job after they booked European football next season.
Ayoze Perez and Demarai Gray struck at the King Power Stadium to beat a subdued Sheffield United.
Leicester remain in pole position to reach the Champions League and finish in the top four ahead of Manchester United, who they host on the final day.
They remain fourth, a point behind Chelsea, but cannot finish lower than sixth to guarantee themselves at least a Europa League spot. However, Rodgers wants more.
He said: "There's two games to go, we've achieved that goal, let's achieve the barrier-breaking goal and get into the Champions League. In my time here that's what I wanted to achieve and to do that first season and guarantee it now is an absolutely phenomenal achievement.
"We have lacked that bit of consistency but there's only one consistent team in the league and that's Liverpool.
"For the boys to guarantee this position with a couple of games to go I just tip my hat to them. It's an amazing achievement."
But in a blow to their top-four hopes Rodgers confirmed injured duo James Maddison (hip) and Ben Chilwell (foot) will miss the rest of the season. Christian Fuchs also faces up to three months out with a hip problem.