The Foxes avoided a third straight Premier League defeat to claim a 2-2 draw against battling Boro who were seconds away from a deserved victory.
Alvaro Negredo had twice put them ahead, with Riyad Mahrez levelling in the first half with his own penalty, but Slimani's last-gasp spot kick saved the Foxes.
Last season's shock title winners are still stuttering in the league having won just once in their last eight games despite a late fightback.
They may have qualified for the Champions League last 16 in midweek but they were poor against vibrant Boro, who gave them a huge scare, and are two points above the relegation zone.
Nothing should be taken away from Boro's performance though after they dominated most of the first half, soaked up pressure after the break and hit the Foxes with what looked to be a sucker punch.
The visitors started with confidence while Leicester lacked the intensity which helped them to a 2-1 win over Club Brugge and into the Champions League knockout stages on Tuesday.
The first warning came when Adama Traore burst into the area and Ron-Robert Zieler palmed his cross out to Marten De Roon to fire wide from the edge of the box.
Claudio Ranieri admitted pre-match he needed to ring his imaginary bell to wake the Foxes up from their slumber but that warning was not heeded and subdued City paid the price when Boro took a deserved lead after 13 minutes.
Negredo started the move when he collected a high ball on the halfway line as Leicester appealed for an offside flag which was never going to come.
He spread it to Gaston Ramirez and timed his run to meet the Uruguayan's low cross and sweep the ball into the top corner from 16 yards.
Sharp in possession and hard-working without the ball, Boro presented a tougher challenge than Club Brugge as Leicester, without the banned Danny Drinkwater, allowed them time and space to continue to dominate.
But the Foxes almost levelled from nothing after half an hour when Shinji Okazaki hit the woodwork.
The previously quiet Mahrez tricked his way into space in the area and delivered a cross for Okazaki to produce a wonderful improvised overhead kick from 12 yards which hit the top of the bar.
It lifted Leicester and they levelled four minutes later in controversial fashion through Mahrez's penalty.
Danny Simpson launched a deep cross and Calum Chambers, who had just been booked for catching Jamie Vardy in the face, handled under pressure from Wes Morgan.
Morgan had certainly given Chambers a shove and referee Lee Mason took an age to decide but eventually awarded the spot kick and Mahrez fired in his seventh goal of the season off the post.
The goal transformed the Foxes and Ramirez had to make a goal-saving challenge when he whipped the ball off Vardy's toes just as it looked like the striker would end his own 14-game goal drought.
Half-time allowed Middlesbrough to regain their composure and while Leicester had improved they still failed to create meaningful chances.
Marc Albrighton headed over after 62 minutes and Ranieri turned to record £30million buy Slimani with 25 minutes left as he replaced Vardy, still looking for a club goal since September 10.
Fellow substitute Ahmed Musa set up Okazaki but Victor Valdes easily claimed his effort and then watched Musa's drive fly over.
But just as Leicester were starting to edge the contest Boro went ahead again with 19 minutes left with Negredo's second.
The Foxes were completely caught out by Adam Forshaw's ball over the top and, with Christian Fuchs playing Negredo onside, the striker raced into the area and planted a fine angled finish past Zieler.
Leicester's initial response was muted and Daniel Amartey's drive flew wide before the midfielder took the ball away from Slimani as he shaped to shoot.
But the Foxes levelled in the third minute of added time when Morgan was fouled in the box by De Roon and Slimani sent Valdes the wrong way.