Eddie Howe’s side had twice fought back from a goal down when defender Nathan Collins appeared inside the box early in the second half to guide the ball into the corner and give the home side a lead that they would not relinquish.
Yet the manner in which Newcastle gifted goals to the hosts will have been cause for frustration.
Harvey Barnes was guilty of losing possession to allow Yoane Wissa to put Brentford 2-1 up, an error for which he quickly atoned to make it 2-2.
Alexander Isak had earlier scored Newcastle’s first equaliser, heading in to cancel out Bryan Mbeumo’s eighth-minute opener and setting the tone for another thrilling, high-scoring home win for Thomas Frank’s side, capped by Schade’s strike in stoppage time.
This was a meeting between 11th and 12th, two sides locked on the same number of points but within a win of the European places before kick-off.
It also pitched a Brentford side enjoying the strongest home form in the division against a team in Newcastle with just two wins on the road, and in atrocious conditions in west London the game swung first towards Frank’s team.
Christian Norgaard drilled a wonderful pass from inside his own half that landed with Mbeumo wide on the right. Lewis Hall stood him up, but Mbeumo backed the Newcastle defender into the box before skating round him and dispatching a left-footed pearler that crashed into Nick Pope’s top corner.
Brentford’s outstanding home form was on course to send another visiting side away empty-handed, but before they could settle into the lead, Newcastle hit back through Isak.
Jacob Murphy’s cross was perfectly flighted, and darting between two defenders to meet it six yards out was the visitors’ top scorer to head his seventh league goal of the season.
Isak ought to have had a second but having walked the ball around Mark Flekken dithered over his finish allowing the goalkeeper to recover and scoop the ball away.
Bruno Guimaraes drove inches past a post with a first-time effort that had Flekken beaten, as after a nervy opening Newcastle steadily took charge.
Yet their control of the game was shot to pieces amidst a woeful lapse in concentration from Barnes, in the team in place of Anthony Gordon but the architect of his team’s downfall.
Under little pressure in midfield, he played the ball blindly infield to the feet of Wissa who charged single-mindedly towards goal before letting rip into the top corner beyond Pope.
This lead was as short-lived as the first and was surrendered more cheaply.
Minutes after the restart, Barnes could scarcely believe his luck, or the space Brentford afforded him inside the box to collect Murphy’s pass, make an about-turn and then roll the ball across Flekken and in.
Brentford had won matches 4-3 and 5-3 here this season and were never likely to be cowed by a second Newcastle equaliser.
In the 56th minute, the game lurched again in their favour, but how Flekken’s long punt forward evaded everyone inside the box and reached the unmarked Collins will have irked Howe, as will the space the defender was given to prod Brentford back into the lead.
Schade got the goal that hoisted the hosts into sixth on goals scored from Brighton, lifting the ball beautifully over Pope from Mbeumo’s pass in stoppage time.