A stunning goal by Anis Mehmeti has left them in danger of sliding out of the two automatic promotion places from the Championship.
The Bristol City winger accepted a square ball from Mark Sykes on the edge of the box and sent a sweet left-footed shot into the roof of the net in the 73rd minute to earn his side a 1-0 victory at Ashton Gate.
Former England striker Jamie Vardy was twice denied by fine Max O'Leary saves when one-on-one with the Robins goalkeeper.
"There would be cause for concern if the performances weren't there," said Leicester boss Enzo Maresca, "But we are creating so much and our recent defeats have all been down to not finishing our chances.
"Jamie Vardy doesn't need to apologise to anyone after all he has contributed over the years. Even the best strikers miss chances. That's football."
The defeat meant Ipswich Town, who were kicking off later on Saturday at Blackburn, with Australian Massimo Luongo in the starting XI, would leapfrog them with a win at Ewood Park.
Fourth-placed Southampton missed the chance to close the gap on the top three after a 90th-minute equaliser from Middlesbrough's Emmanuel Latte Lath cancelled out Adam Armstrong's early opener in a 1-1 draw.
Sixth-placed Norwich came from behind to beat lowly Plymouth 2-1. Arygle had led through Morgan Whittaker's 10th-minute opener but Josh Sargent equalised before an own goal from Ashley Phillips in the 74th minute.
Coventry and Preston both kept alive their hopes of snatching a play-off spot with victories over Huddersfield and Rotherham respectively.
Jimmy Dunne's injury-time volley gave QPR a dramatic 2-1 victory in the big battle at the bottom against Birmingham.
Birmingham remain just outside the bottom three after Sheffield Wednesday were pegged back in a 1-1 draw with Swansea.
Stoke gained a precious 2-0 win at play-off chasing Hull, Sunderland won by the same score at Cardiff and West Brom drew 1-1 at Millwall.
