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Penalty failure costs Seagulls
Ashley Barnes had a second-half penalty saved as Albion lost away to the Championship leaders.
Kasper Schmeichel got down to his left to block Barnes' 55th-minute spot and secure a 1-0 win for Leicester at the King Power Stadium.
City also owed their sixth win out of six at home to a powerful start to the match.
They piled on early pressure and went ahead when Andy King burst through in the tenth minute.
Albion were more of a threat after the break with Will Buckley involved in their best moments.
The winger was fouled by Zak Whitbread but Barnes saw his penalty saved and then fired the rebound over the bar at full stretch.
There were chances at both ends after that but Barnes drilled the last of them just past the post deep in added time as the Seagulls failed to score for the third successive match.