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Pickford has been under scrutiny for the last year after some increasingly erratic displays.
Everton manager Carlo Ancelotti has largely kept faith with Pickford, but that patience will be sorely tested by yet another mistake.
Clinging to the first half lead given to them by James Rodriguez, Everton were denied three points when Pickford let Tielemans' shot squirm into the net after the break at Goodison Park.
It was no more than Leicester deserved for an enterprising display that merited all three points.
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Leicester are now unbeaten in nine matches in all competitions since losing at home to Everton in December.
They sit third in the Premier League, two points behind leaders Manchester City, and look capable of pushing for a top four finish even with leading scorer Jamie Vardy currently sidelined through injury.
Rodriguez, Dominic Calvert-Lewin and Richarlison started together for Everton for the first time since December 5.
But it was Leicester who made the brighter opening.
After James Justin stole possession for the visitors, James Maddison's dipping long-range shot landed on the roof of the net.
Leicester were dominating with some smooth passing and movement.
However, having weathered the Leicester onslaught, Everton broke out to snatch the lead in the 30th minute.
Rodriguez's shot was weakly blocked by Wesley Fofana and the Colombian midfielder seized the ball again before curling a superb shot past Kasper Schmeichel from the edge of the area.
It was Rodriguez's first goal since October and just his fourth following his September move from Real Madrid.
There was another blow to Leicester when Nigerian midfielder Wilfred Ndidi was forced off with an injury.
Leicester's frustration was mounting and Schmeichel could be heard screaming "we're better than this" after they squandered possession too easily before the break.
Scalded by their keeper and presumably reminded of their responsibilities by boss Brendan Rodgers, Leicester regained their composure in the second half.
They poured forward and nearly equalised when Harvey Barnes' blast forced a good save from Pickford before Justin steered the rebound just wide.
Leicester's pressure was finally rewarded as Pickford gifted them the 67th minute leveller.
Pickford was guilty of flapping at Barnes' cross and when the ball was recycled to Tielemans on the edge of the area, the Belgian's shot through a crowd of players should have been held by the England keeper.
Instead, although he got both hands behind the ball, it squirmed through his grasp and into the net.
England manager Gareth Southgate, watching from the stands, was surely as unimpressed as the grimacing Ancelotti.
Pickford did save Maddison's deflected effort to deny Leicester a winner, but the damage had already been done.
smg/dj