For the first time in three years, Hart's position as England's number one has come into question after a series of sub-par performances for club and country.
The 26-year-old, who has 35 caps, did not perform at his best against Scotland in August and he has since made notable errors in Manchester City's games against Cardiff, Aston Villa and Bayern Munich.
Given that they need two wins in their final two games to guarantee their qualification for the World Cup, England cannot afford any more slip-ups.
But if either Montenegro or Poland view Hart as England's weak link then they are mistaken, Jagielka claims.
"There is no question in my mind how Joe will react and how he will perform," the England defender said.
"He is a fantastic goalkeeper and a fantastic lad.
"If he does make a bad decision the ball ends up in the back of the goal - he knows that is part of the territory for him.
"He sets massively high standards for himself and when it doesn't go for him people are quick to jump on his back.
"He knows he has the full backing of the whole squad and I am sure he is delighted to be here and he is looking forward to playing."
With England just one point ahead of Ukraine and Montenegro, the only way Roy Hodgson's men can guarantee direct qualification is with victories against Montenegro on Friday and Poland four days later.
Of all the players in Hodgson's 23-man squad, Jagielka has to be one of the most desperate to make it to Brazil.
The Everton captain made his England debut in 2008, but missed out on the 2010 World Cup squad and then did not play a single minute of the Three Lions' Euro 2012 campaign despite travelling to Ukraine and Poland.
The 31-year-old was part of the England team that drew 2-2 in Rio de Janeiro at the end of last season.
Playing in the Maracana and walking along the sandy beaches of the Copacabana clearly whetted his appetite for competing in next summer's tournament.
"We went over there in the summer and we tasted the atmosphere and the heat and it was quite incredible," the centre-back said.
"Playing in a World Cup is something I am desperate to do. I haven't played in any sort of finals.
"Obviously I got the chance to travel to Euro 2012, which was a good experience, but the clock is ticking. I am not getting any younger so it would be nice to help the team book their ticket over there and then hopefully I will put my name in to the hat for the squad if I stay injury-free."
England have struggled through their qualification campaign so far, with their only wins coming against the joint-worst nation in the world San Marino, and Moldova, who are sandwiched between Tanzania and Guyana in the rankings.
But Jagielka says the mood within the camp is one of quiet confidence, borne mainly out of the fact that Hodgson has in-form strike duo Wayne Rooney and Daniel Sturridge available.
"We have to be confident that we can get the job done," the former Sheffield United man said.
"The squad looks healthy. Roy has gone very attacking in this squad and he has lots of options.
"All the strikers looked sharp in training - I know that for a fact - so the manager has a tough decision to make there."
One simple decision Hodgson has to make is at left-back, where Leighton Baines is almost certain to come in for the injured Ashley Cole.
"I am sure he won't let us down," Jagielka said of his Everton team-mate.
"He is a good defender and he gives us another attacking threat down the left flank as well."