The former Hull City winger struck twice inside the opening 10 minutes before Neal Maupay found a quick reply for the Bees, but the visitors' lackadaisical defending continued to prove costly as Bowen became the first West Ham player to score a Premier League treble at the London Stadium.
An Emerson Palmieri stunner then preceded a Yoane Wissa consolation to cap off a spectacular six-goal London derby, one which saw David Moyes's men pick up their first Premier League win of 2024 and also beat Brentford in the top flight for the first time.
For the first time since December, Lucas Paqueta started a Premier League game for West Ham following his calf injury, while Keane Lewis-Potter, Maupay and Mathias Jensen forced their way back into the Bees' XI.
Each of the five Premier League meetings between West Ham and Brentford had seen the Bees emerge victorious, but thanks to a marvellous start beyond Irons' expectations, Moyes's men took two giant steps towards ending that hoodoo.
Just one moment after Tomas Soucek blazed a promising chance over the bar, Edson Alvarez robbed Frank Onyeka of the ball and sparked a rapid West Ham attack, which ended with Bowen finding a gap at Mark Flekken's near post with an outside-of-the-foot slice in the fifth minute.
Only two minutes after getting the London Stadium crowd off their feet, Bowen was the beneficiary of more sloppy play from the Bees; after Zanka cheaply conceded possession, the Hammers worked the ball from left to right, and the Englishman arrived to fire in from Vladimir Coufal's low ball into the box.
The hosts' stay in dreamland did not last long, though, as a shell-shocked Brentford cut the deficit in half with 13 minutes on the board, as Lewis-Potter spotted a clever horizontal run from Maupay across the edge of the box and slipped in the Frenchman to find the roof of the net.
Another defensive mishap was to blame for another early goal - Kurt Zouma gave the ball away and left acres of space for Lewis-Potter to exploit - and the game unsurprisingly began to slow down after such a frenetic opening.
There was time for a familiar dose of controversy in the 16th minute, though, as Mohammed Kudus barged Sergio Reguilon over just inside the penalty box, but neither Simon Hooper nor the VAR room were interested.
The hosts outgunned Brentford significantly on the shot front as the first half progressed - firing 14 compared to two for Thomas Frank's men - but wastefulness was harming their prospects of restoring their two-goal advantage.
The Bees were still just a goal down heading into the second half, although they were fortunate not to be a man down in the 54th minute, as Reguilon - already on a yellow card - needlessly clipped Soucek's legs from behind, but Hooper's cards remained in his pocket.
Brentford would lose a defender just after the hour mark, though, as Ben Mee could not continue due to a whack to the foot - Nathan Collins took his place - and just two minutes after losing their fan favourite centre-back, the visitors conceded again.
Another cross from the right did the damage for West Ham, as Kudus's delicate inswinger found the head of Bowen, who was totally unmarked and guided the ball into the bottom corner beyond a stranded Flekken to complete a landmark hat-trick in the 63rd minute.
Frank's men still had a flicker of life left in them and came close to another instant reply in the 66th minute, but Alphonse Areola was equal to Onyeka's near-post volley, and only another three moments passed before West Ham found their fourth in incredible fashion.
Brentford only managed to clear another Kudus delivery as far as Emerson 25 yards from goal, and the left-back took one touch to set himself before unleashing a thunderbolt into the top corner.
Not all West Ham fans would have been sitting comfortably in the final few moments, as Wissa managed to stay onside and curl a deft strike into the bottom corner in the 82nd minute, and the visitors were gifted seven minutes of additional time to try to complete an astonishing fightback.
Such a turnaround did not materialise - thanks in no small part to a tremendous Areola save from Ivan Toney's close-range header - as the Europa Conference League champions clung on for the success which moved them up two places into eighth spot in the table, while Frank's men are in 16th and just five points clear of the drop zone owing to Everton's deduction being reduced to six.
West Ham hit the road again on Saturday, travelling to Everton for a 3pm kickoff, the same time that Brentford host Chelsea in a West London derby.