"This is the right moment to push," said manager Ranieri, whose team need a maximum of five points from their final three games to secure the title.
"I talked to my players before the game and said that it has been a dream so far, so now make the dream reality."
He added: "I told them give everything then we won`t regret."
No Vardy, same party
Leicester faced Swansea without striker Jamie Vardy, who was suspended.
Any doubts that the Foxes would struggle without their 22-goal top scorer were removed as Leonardo Ulloa, his replacement, scored twice after Riyad Mahrez`s opener.
Marc Albrighton completed the scoring to give Leicester their biggest of the season.
"This was an important win because everybody wanted our answer without Vardy - and that was a fantastic answer," added Ranieri.
"Ulloa was fantastic. He held the ball up, attacked and defended and scored two goals, so well done to him. He was top scorer last season and he doesn`t lose his ability."
Spurs `as fresh as day one`
The win puts pressure on Tottenham, who play West Bromwich Albion on Monday.
Anything less than victory for Spurs means Leicester will be confirmed as Premier League champions by beating Manchester United at Old Trafford on Sunday.
Tottenham boss Mauricio Pochettino warned that he does not expect his side to slip up, saying: "I think we are as strong as at the start of the season.
"The data is similar at the beginning to now, because now we can see the finish line.
"We haven`t arrived yet, this is important, but our motivation is good and then you can run more. It is always in our mind and we are in a very good moment.
"We need to fight to achieve big things like winning the title."
