Leonardo Ulloa’s 89th-minute goal extended Leicester’s lead at the top of the Premier League to five points and denied Norwich a deserved draw.
Ulloa slid in at the far post to convert Marc Albrighton’s cross at the end of an otherwise limp Foxes display.
Norwich earlier had the better chances, Cameron Jerome heading wide and Nathan Redmond off target from distance.
Leicester had largely been restricted to shots from distance until substitute Ulloa had the final say.
Until the Argentine’s intervention, the Foxes were facing the prospect of losing top spot if either of Arsenal or Tottenham win on Sunday – instead they are guaranteed to remain at the summit with 11 games remaining.
Norwich are still outside the relegation places, but level on points with Newcastle, who have a game in hand.
Meanwhile,Chelsea moved up to 11th after coming back from a goal down to beat Southampton courtesy of a Branislav Ivanovic header.
Shane Long headed high for the home side but atoned when he pounced on a Baba Rahman blunder before clipping a shot over keeper Thibaut Courtois.
Diego Costa volleyed wide for Chelsea but the visitors equalised when a Cesc Fabregas cross crept in.
Chelsea finished strongly and Ivanovic headed in from a Willian corner.
Over in La Liga, Zinedine Zidane suffered his first defeat as Real Madrid coach, as Antoine Griezmann gave local rivals Atletico Madrid a 1-0 victory at the Bernabeu.
The Frenchman struck in the 53rd minute to inflict a fourth league derby defeat in six games on the Merengues, who have not managed to beat their local rivals in the Primera Division since 2013.