The Foxes went ahead in the third minute when Jamie Vardy pounced on a defensive error and teed up Harvey Barnes.
Tielemans made the score 2-0 on 21 minutes, following up after Vardy's header had been saved by Illan Meslier.
Patrick Bamford's close-range effort for Leeds was saved by Kasper Schmeichel before the break.
Three minutes after half-time, Stuart Dallas's curling delivery sneaked in at the far post to give Leeds hope.
But substitutes James Maddison and Cengiz Under combined superbly for Vardy to restore Leicester's two-goal cushion on 76 minutes.
Following a foul by Mateusz Klich and a VAR check, Tielemans stroked in a stoppage-time penalty to cap the win.
Leeds drop to 12th on 10 points, Leicester are now one behind league leaders Liverpool.
Budweiser King of the Match: Jamie Vardy (LEI)
Leeds: 7 Nov v Crystal Palace (A)
Leicester: 8 Nov v Wolves (H)