After Bryan Mbeumo's early disallowed goal, Guimarães got the Magpies on their way at St. James' Park, heading home a Kieran Trippier cross.
Jacob Murphy tapped home a second before the break and, although Ivan Toney pulled one back for the Bees from the spot, further efforts from Guimarães, Almirón and Pinnock's last-minute miscue added extra gloss to the scoreline.
The result means Eddie Howe's side have now scored nine goals in their last two Premier League outings, following last weekend's 4-1 thrashing of Fulham.
Another swift start from the hosts saw Almirón whip in a shot which Raya turned round the post in acrobatic fashion, but the game's first real talking point came after ten minutes. Some neat build-up play culminated in a clever flick which freed Mbeumo, whose shot sneaked past Nick Pope and into the bottom left-hand corner. After a VAR check, however, referee John Brooks - who went to view the goal on the pitchside monitor - felt former United forward Toney was offside as he stepped out of the way to allow the ball to reach Mbeumo, and disallowed the goal.
It felt a little harsh on the visitors but they could have few complaints at the manner in which they fell behind midway through the half, as they were carved open by a well-worked United set piece. Almirón played a corner back to Trippier, whose perfect deep cross was met by the unmarked Guimarães. The Brazilian's diving header was firm and despite Raya getting a touch, the Bees' keeper couldn't prevent it dropping in via the upright.
That was Guimarães' first of the season and it signalled a spell of pressure, with Murphy seeing a low effort stopped by Raya after a quick breakaway. But just before the half hour mark, it was two, and it was a goal which came courtesy of both a Raya error and Callum Wilson's cool head. Brentford's Spanish stopper inexplicably miscued his pass under little pressure, skewing it straight to Wilson on the edge of the box. The forward showed great composure to carry the ball forward, commit Raya and square for Murphy, who had the simple task of rolling the ball home.
With the scoreline at 2-0 at half time, the Magpies looked in total control, but nine minutes after the restart the visitors were handed a lifeline. After Mbeumo saw a shot parried by Pope, Dan Burn was penalised for handball as Brentford pushed forward briefly. Toney, who made just three appearances during his time at St. James' Park, stepped up to sweep home from the spot and fuel the Bees' hopes of a comeback.
But just two minutes later, their faint hopes of a recovery were dashed by another moment of quality from Guimarães. Brentford got themselves stuck in their own half, with Aaron Hickey off-balance and trying in vain to hold onto possession. Newcastle's number 39 robbed him and drove forward, waiting for a gap to open up and when it did, he struck. The 24-year-old's swerving low strike found the corner, beyond the reach of Raya, and put the result beyond doubt.
Substitute Joelinton then combined with Joe Willock to create an opening, with the former Arsenal man bursting into the area and seeing his effort charged down, but United would have their fourth goal in the end - and it was another gift. Pinnock's misjudgement of his pass back to Raya let Almirón in, and he duly slammed home after rounding the goalkeeper to make it four.
And the scoring didn't stop there. It was the final minute by the time Joelinton made it to the byline and sent over a low cross, which the luckless Pinnock reached first, diverting the ball away from Raya and into the bottom corner to round off a fine day for those in black and white.
