Alvaro Negredo ended a goal drought which stretched back to the opening day of the season when he put Boro ahead following a neat exchange of passes with Gaston Ramirez.
Riyad Mahrez equalised from the penalty spot after Calum Chambers was judged to have handled.
Negredo looked to have given Boro the points when he latched on to a long ball and clinically dispatched a low shot past Foxes goalkeeper Ron-Robert Zieler.
But Slimani converted from the spot in the fourth minute of injury time after Wes Morgan was fouled by Marten de Roon.
There were murmurs of discontent from the home fans at the King Power Stadium, but Leicester’s players rolled up their sleeves and fought right to the final whistle.
For large parts of the game, the Foxes lacked any kind of zip or purpose about their play. Crucially, though, they kept going and salvaged a point.
It came on the back of Tuesday’s 2-1 win over Club Brugge, which secured their passage to the knockout stages of the Champions League with a game to spare.
Importantly, it ensured Leicester did not slip to a third successive Premier League defeat.
“We showed fantastic character,” said Ranieri. “Lucky is someone who believes in something more.”
Negredo ends goalscoring drough
Negredo, who is on a season-long loan from Valencia, found the net for the first time since Boro’s 1-1 draw against Stoke City on 13 August.
It was not just the powerful Spaniard’s finishing that caught the eye at the King Power Stadium either.
Negredo held the ball up, linked up the play and was generally a handful for the Leicester defence.
He scored 23 goals in 48 appearances for Manchester City en route to helping them win the Premier League title in 2013-14.
Given his side’s overall lack of goals this season, Boro boss Aitor Karanka will hope it represents the start of a hot streak for Negredo.
While Negredo was back among the goals, Jamie Vardy’s struggles to find the net continue.
Vardy has not scored for the champions since 10 September – a run of 15 games. His form is in stark contrast to a year ago, when he scored for a record 11th Premier League game in a row.
Without Danny Drinkwater, suspended for three matches for elbowing Watford’s Valon Behrami, Leicester relied too often on high balls, which did not utilise Vardy’s strengths.
But irrespective of that, Vardy’s performance was subdued, as was his body language.
He could have few complaints when substituted with 25 minutes left.