The Magpies netted twice in the opening 13 minutes at the London Stadium courtesy of Callum Wilson's header, the striker's fourth goal in as many starts against the Hammers, and Joelinton's composed finish after a VAR review but had almost conceded within the first minute as Bruno Guimarães inadvertently turned Jarrod Bowen's cross onto his own post.
Kurt Zouma's close-range header halved the deficit before the half-time break before Wilson's close-range tap-in, 22 seconds after the restart, restored the visitors' two-goal cushion.
Alexander Isak, introduced from the substitutes' bench, added Newcastle's fourth after lifting the ball into the net from distance, capitalising on Łukasz Fabianski's error, before Joelinton's low finish added gloss to the scoreline in the final stages to seal a fourth successive Premier League victory.
Eddie Howe made two changes to the side which claimed an impressive 2-0 win against Champions League chasing Manchester United on Sunday as Wilson, who had scored ten goals in his last 12 outings against West Ham before this evening's clash, started ahead of Alexander Isak while Joelinton was handed a start in place of Joe Willock.
The visitors, aiming to maintain third spot in the table by securing maximum points in Stratford, were fortunate to remain on level terms within the first minute of the 50th Premier League encounter between the two sides as Bowen advanced past Dan Burn before his low cross was fired onto the post by Guimarães before Sven Botman cleared the loose ball to safety.
In the 6th minute, Newcastle took the lead as Wilson netted his ninth league goal of the season. After Saint-Maximin curled a inviting cross into the penalty area, the unmarked striker was on hand to guide his header past Hammers goalkeeper Fabiánski into the far left-hand corner.
The Magpies doubled their advantage seven minutes later as Joelinton notched his first league goal since United's 3-0 victory at Leicester City on Boxing Day. After Fabian Schär fired a dangerous ball in behind the Hammers defence, the Brazilian calmly rounded Fabiánski before slotting the ball into an empty net and, following a VAR review, the goal stood to the delight of the 3,000 travelling away supporters.
Nick Pope, targeting a 14th Premier League clean sheet, was forced into making an important save to deny Lucas Paquetá as the England international pushed the Brazilian's goal bound free-kick around the left-hand post.
Sven Botman produced a crucial last-ditch tackle to block Michail Antonio's powerful drive at goal, anticipating the Jamaica international's run inside the box to crucially turn the ball out for a corner.
West Ham reduced the deficit in the 40th minute through Zouma as the French centre-back latched onto Bowen's in-swinging cross before heading the ball into the roof of the net.
Newcastle got off to a flying start in the first minute of the second-half as Wilson recorded his tenth goal of the season in simple fashion. After Jacob Murphy dispossessed Nayef Aguerd on the edge of the box, the winger unselfishly teed up Wilson who placed the ball into the net, moving into the top ten of the club's all-time leading goalscorers' list in the process.
The Magpies went close to adding a fourth in terrific fashion as Sean Longstaff's diagonal pass found its way to Saint-Maximin, who exchanged crisp passes with Joelinton before the Frenchman set up Murphy, who saw his first-time effort saved by Fabiánski.
Saint-Maximin almost netted his first goal since August as the left winger's bending effort from the edge of the box was pushed around the far post by the fingertips of Fabiánski.
Guimarães created a key opportunity to extend Newcastle's lead further as the Brazilian midfielder controlled Joelinton's pass on the edge of the penalty area before his fierce shot at goal flew narrowly past the left-hand post.
Howe completed a triple substitution shortly after the hour mark as Willock, Anthony Gordon and Isak were introduced from the bench and it was the latter who got his name on the scoresheet in the 82nd minute.
As Fabiánski rushed from his goalline to attempt clearing Guimarães' pass, the Pole handed the ball to Isak, who lifted the ball into the net from distance to register his seventh goal in 12 league matches.
Joelinton rounded off an excellent display in East London with his second goal of the evening, controlling Guimarães' forward pass before, after advancing into the box, firing a low effort into the far right-hand corner to equal the club's biggest ever Premier League away win since a 5-1 thrashing of Coventry City in September 1998.
