The Foxes climbed to third in the Premier League as they continued their unbeaten start with a 3-1 win at the King Power Stadium.
England striker Callum Wilson’s first goal of the season had initially pulled Bournemouth level in the first half.
Tielemans also escaped a second-half red card after a VAR check when he went over the ball to catch Wilson on the ankle.
The Cherries would have had every right to feel aggrieved with VAR again under the spotlight.
As it was they slipped to 14th after suffering successive defeats.
Eddie Howe’s men started well enough but were behind after 12 minutes.
Yet the Cherries hit back within three minutes when Wilson clipped the ball in off the post from eight yards after latching onto Ryan Fraser’s pass.
An open start continued with James Maddison heading wide after 21 minutes and Ramsdale got lucky when his sloppy clearance cannoned off Vardy before the goalkeeper grabbed the ball ahead of the striker.
Maddison’s movement, along with Vardy, Tielemans and Harvey Barnes, caused the Cherries problems and the two combined to restore Leicester’s advantage four minutes before the break.
Vardy failed with his initial cross but got a second chance to slide the ball across the six-yard box for Tielemans to stab in off the post from close range.
It was the midfielder’s first goal since he returned from Monaco – following last season’s loan – for a club record £40milllion in the summer.
But Tielemans could have walked 10 minutes into the second half yet avoided a red card, after a VAR check, when he went over the ball and caught Wilson on the ankle.
The let-off allowed Leicester to press for a third and Ramsdale turned away Barnes’ 18-yard effort before Vardy grabbed his second after 73 minutes.
Mepham then presented the ball to Tielemans to find Vardy, who steered in from six yards.