The Argentinian forward came off the bench to turn home Marc Albrighton’s cross from close range in the 89th minute.
It was just his third goal of the season and broke stubborn Norwich’s resistance.
The forward has only started five league games this season with 19-goal Jamie Vardy and Shinji Okazaki Ranieri’s first-choice strikeforce.
But Ranieri insisted the former Brighton man, and the rest of his squad, are united as they chase the top prize.
“Ulloa is happy but everyone is happy. When one man scores a goal, all of Leicester City Football Club are happy,” he said.
“Everybody is happy because the team is playing well and is top of the league.
“Everyone would like to play, but it’s not possible. They believe in the project and they believe their team-mates are playing well.
“For me it’s important to believe in them because, when I need some changes, they are ready.
“For this reason I’ve said many times we have a fantastic dressing room.”
Norwich had frustrated the Foxes for long spells and looked on course for a priceless point in their fight for survival before Ulloa’s winner.
Vardy and Riyad Mahrez were silenced by the gritty Canaries and denied any clear chances with the Foxes well below par.
But Ranieri admitted he would happily take substance over style in the title run-in.
“You cannot always play well, it’s not important to play well or not, it’s important to take points.
“We wanted to re-start. We believe in ourselves, we believe until the end that it’s important to fight. We lost a match in the last second against Arsenal and today we won in the last minute. That’s football.
“We expected a battle. I want to say well done to Norwich because it was a good battle. The first half we tried to find a solution but it was difficult because Norwich played to maintain the clean sheet.
“With 20 minutes to go it was an open match; we can score, they can score. I tried to make some changes to spread out the defensive line. It was a good choice.”
Leicester host West Brom tomorrow and then go to Watford on Saturday as they look to continue their shock title challenge and Ranieri will assess N’Golo Kante after the midfielder came off injured against the Canaries.
He added: “He had just a little pain in his hamstring and we will check.”
Defeat left Norwich with seven losses in their last eight games in all competitions and only out of the relegation zone on goal difference.
Manager Alex Neil said: “If Leicester were the better side and deserved the win you take your humble pie, regroup, and get ready for the next game.
“In recent weeks we have been 2-0 up against West Ham, 3-1 on Liverpool and on Saturday we had a great opportunity to get a point or maybe three.
“We’ll take a lot of heart from the performance. We’ll look at the game and know we should have got something better than what we did. We have a big game on Tuesday now (against Chelsea) and if we can fight and scrap, create as many chances as we did today and keep the opposition quiet we’ll have a good chance.”
Schmeichel, Amartey (Ulloa 78), Morgan, Huth, Fuchs, Mahrez, Drinkwater, Kante (King 70), Albrighton, Okazaki (Schlupp 69), Vardy.
Gray, Dyer, Wasilewski, Schwarzer.
Ruddy, Ivo Pinto, Bennett, Martin, Klose (Mbokani 90), Brady, Redmond, Tettey, Howson, Naismith (Jarvis 82), Jerome (Bamford 90).
Rudd, Mulumbu, Olsson, O’Neil.