Leicester trailed twice to goals from Negredo, but Mahrez equalised with a penalty before Slimani scored.
Leicester salvaged a dramatic 2-2 draw against Middlesbrough as Islam Slimani converted a penalty deep into stoppage-time at the King Power Stadium on Saturday.
Claudio Ranieri's side trailed twice to goals from Middlesbrough striker Alvaro Negredo, but Riyad Mahrez got Leicester's first equaliser with a penalty before his Algerian team-mate Slimani struck from the spot to earn a point with virtually the last kick of a thrilling encounter.
Although Leicester finished the happier thanks to their late escape, the Foxes remain too close to the relegation zone for comfort and their fairytale title seems a lifetime ago just seven months later.
Middlesbrough went into the match as the Premier League's joint lowest scorers, but they threatened first as Adama Traore sped past Christian Fuchs and drove in a cross-shot that Ron-Robert Zieler parried to Marten de Roon, who swept his effort wide.
Karanka's team had found their stride quickly and Negredo's 977-minute goal drought came to an end in the 13th minute.
Negredo, on loan from Valencia, had gone 11 games without a goal since scoring in the opening game of the season, but the Spanish striker was in unusually clinical mood as he exchanged passes with Gaston Ramirez and fired high into the net from inside the penalty area.
Leicester's 2-1 Champions League win over Brugge in midweek was the latest memorable moment in their maiden voyage in Europe's elite club competition.
Ranieri's men have been far less inspired in their title defence, but they roused themselves after falling behind and Japan striker Shinji Okazaki hit the bar with a spectacular scissor kick from Mahrez's cross.
The Foxes' pressure was rewarded with a 34th minute equaliser when Middlesbrough defender Calum Chambers was penalised for handball and Mahrez stroked home the spot-kick.
After scoring 13 times by this stage last season, Leicester striker Jamie Vardy has found himself stuck in a rut with 14 games without a goal since he netted his second of the campaign on September 10.
Vardy could have broken his barren streak when Okazaki crossed towards him just before half time, but Ramirez cleared as the England international prepared to shoot.
It would prove another frustrating afternoon for Vardy, who was booked and never looked likely to get on the scoresheet before being substituted midway through the second half.
Vardy was replaced by Slimani and Mahrez also departed as Ranieri tried to pep up his attack, yet Middlesbrough regained the lead in the 71st minute.
Adam Forshaw's high pass over the Leicester defence sent Negredo racing clear and he fired a low strike past Zieler.
To their credit, Leicester responded well to that setback and Daniel Amartey went close before the equaliser arrived in the fourth minute of stoppage-time.
De Roon fouled Wes Morgan in the penalty area and Slimani calmly slotted home to rescue the champions.