That outcome was harsh on the visitors, who were the better side for long spells and appeared destined for victory when Alvaro Negredo netted his second of the afternoon midway through the second half.
The Spaniard had put his side ahead on 13 minutes before Riyad Mahrez drew Leicester level before half-time from the penalty spot.
Leicester yet against failed to reproduce their European form on the domestic scene and they were behind through a fortunate Negredo finish before the quarter hour.
Gaston Ramirez received the ball from the big striker on the left and galloped forward before applying a low centre into the path of Negredo, who slightly mistimed his shot but still saw it fly into the top corner.
Aitor Karanka's side were controlling the game with ease but got their first warning on the half hour when Mahrez teased his way into the penalty box before standing up a cross that Shinji Okazaki acrobatically volleyed on to the crossbar.
Just five minutes later and the champions were given a reprieve. Callum Chambers handled in the box and Mahrez crashed his spot-kick home off the base of the post.
After the break, Andy King had the best opportunity to put the Foxes in front but couldn't keep his header down after Danny Simpson's right-wing cross.
Slimani and Ahmed Musa came on to replace Jamie Vardy and Mahrez and they quickly combined on the edge of the box, with the latter shooting just over.
Leicester were caught napping 18 minutes from time when Adam Forshaw's long ball over the top picked out Negredo to shoot low and hard beyond Robert Zieler to restore Middlesbrough's lead.
In stoppage time, Christian Fuchs' cross was headed into the path of King by Simpson, but the right-back elected to head across goal when he might have scored himself, and Boro cleared.
That looked to be game over, but Wes Morgan was tripped by Maarten De Roon in the final minute of stoppage time and Slimani stepped up to grab a point for Leicester from 12 yards.