Best, making his first Barclays Premier League start for the club in the absence of the injured Carroll and Shola Ameobi, finally opened his account on his 15th appearance with a fine hat-trick to repay a large slice of his £1.2million transfer fee.
They were the 24-year-old's first goals in a week short of a year and came on the day it was revealed Newcastle had rejected an approach from Tottenham for Carroll.
Best's first-half brace and skipper Kevin Nolan's 45th-minute strike put the Magpies in the driving seat, and his third on the hour completed a first double of the campaign and ended the Hammers' recent revival before Peter Lovenkrands helped himself to a fifth.
It was the third time this season Newcastle had scored five or more at St James' Park, and substitute Nile Ranger passed up a glorious opportunity to match the six they managed against Aston Villa back in August.
There was an air of anxiety when it was revealed that Ameobi had joined Carroll in the treatment room.
However, manager Alan Pardew had insisted that both Best and Ranger would get chances this season and his faith in the former Coventry man proved spectacularly well-founded.
Best made his first appearance of the season as a substitute at the DW Stadium at the weekend after a miserable run of injuries had hampered his progress on Tyneside.
But he needed just 18 minutes to justify his selection when he ran on to Lovenkrands' ball over the top to thump a left-foot volley across Robert Green and into the bottom corner.
West Ham had arrived in the north east buoyed by a run of four league games without defeat, but in the relegation zone as a result of victories for Fulham and Birmingham on Tuesday.
Former Magpie Scott Parker had earlier tested Steve Harper with a swerving shot and he attempted to stamp his authority on the midfield battle as the visitors looked for a way back into the game.
However, Cheik Tiote and Joey Barton recognised the danger and started to close Parker down, and with Jonas Gutierrez and Jose Enrique teaming up to terrorise the Hammers down their right, the home side were threatening at regular intervals.
They increased their lead six minutes before the break when a quick-thinking Barton and Lovenkrands carved the sleeping visitors open from a free-kick.
Barton picked out the Dane's run into space and when he slid the ball across goal, Best was again on hand to fire home left-footed.
West Ham's woes deepened markedly on the stroke of half-time when Gutierrez once again found space down the left and sent in a low cross which James Tomkins could only stab out to Nolan two yards inside the penalty area.
Nolan was a model of composure as, with Green desperately trying to recover his ground, he sidefooted the ball firmly into the bottom corner.
Hammers boss Avram Grant sent on Valon Behrami and Victor Obinna for Radoslav Kovac and Frederic Piquionne at the break in a desperate attempt to breathe new life into his team as Mike Williamson replaced Steven Taylor for the Magpies.
But despite Parker's continuing industry they were unable to create anything of note, and Newcastle killed off any hope of a fightback with 30 minutes left when Nolan turned Enrique's pass into the unmarked Best's path and he completed his hat-trick with aplomb.
Lovenkrands added a fifth three minutes later and there was still time for Ranger to fire horribly wide with the goal at his mercy 10 minutes later with the Hammers in tatters.