La Roja began the match in third place, but with just four points separating second from seventh heading into a dramatic night and only three more automatic qualifying places available, Chile's three-goal losing margin ensured that they finish in sixth place, behind Peru on goal difference.
The hosts took the lead with a quickfire double in the space of two second-half minutes as Paulinho and Gabriel Jesus got on the scoresheet, with the latter proving particularly damaging as Chile fell out of the top five as a result.
Jesus then added a late third in stoppage time to pour salt into the wound for the reigning Copa America champions, who are left to contemplate a summer without the World Cup just months after reaching the final of the Confederations Cup.
Brazil, who qualified all the way back in March to become the first team aside from hosts Russia to seal their place at next summer's tournament, handed a debut to Ederson in goal and the Manchester City shot-stopper was called into action as early as the third minute when he made a routine save to deny Eduardo Vargas.
It was not a sign of things to come, however, as numerous fouls broke up the rhythm of the opening stages and the main action unfolded elsewhere with Argentina overcoming an early goal to take the lead against Ecuador in their own must-win clash.
The first clear chance of the opening 45 minutes fell the way of Brazil in the 16th minute when Gonzalo Jara's loose pass gifted the ball to Paulinho, who immediately released Jesus through the middle. The Manchester City striker - playing at the home of his former club Palmeiras - in turn slid the ball to Neymar, who was only denied by a good save from the onrushing Claudio Bravo.
Alexis Sanchez and Neymar both saw speculative efforts from range fly off target as the two star players looked to provide something special in an otherwise scrappy encounter.
Brazil should have broken the deadlock with six minutes remaining of the half, though, when Renato Augusto's cross found Jesus in space inside the area, only for the striker to steer his header straight at Man City teammate Bravo.
Scorelines elsewhere left Chile in the final automatic qualification spot at the interval, but that position did not last long after the restart as Brazil scored twice in quick succession to plunge Juan Antonio Pizzi's side into trouble.
The first arrived 10 minutes into the second half when Dani Alves went for a goal with a long-range free kick that Bravo could not hold, spilling the ball straight to the feet of Paulinho, who was left with a simple finish from the rebound.
The second was more skilfully crafted as Philippe Coutinho's long pass over the top was expertly collected by Neymar, who unselfishly laid the ball across for Jesus to tap into a largely empty net.
Chile almost responded immediately when Sanchez steered an effort narrowly wide, but on the whole there was a disappointing response from the visitors considering the damaging nature of the goals.
Instead, a lack of discipline cost them more valuable time and it was Brazil who looked most like adding to the scoring, with Neymar coming close twice for the home side.
Pizzi's men did finally create a chance of note with a little over 10 minutes remaining when Gary Medel found space inside the area, but the former Cardiff City man headed his effort over the crossbar when he should have done better.
Even in the closing stages it was still Brazil who looked most threatening, and Bravo needed to deny Roberto Firmino before Tite's side capped off the scoring with the final nail in Chile's coffin late on.
With Bravo up the pitch for a stoppage-time corner, Brazil quickly broke and Jesus found himself alone in the Chile half to run the ball into the back of the net and seal La Roja's fate.
Victory for Argentina and a draw between Peru and Colombia meant that Chile dropped three places on the final matchday to finish sixth in the standings, missing out on a playoff spot to Peru by just two goals.
It is the first time Chile have failed to qualify for a World Cup since 2006, whereas five-time champions Brazil end the campaign 10 points clear having won 10 of their 12 qualifying games under Tite.