Newcastle's problems have been laid bare over the first three months of the season, with supporters given little to cheer about by a toothless attack that had not scored more than once in any of their opening 10 Premier League games.
That all changed in an almost-perfect away day for the Toon Army.
Steve Bruce's side were organised defensively and rarely threatened until the Hammers' late fightback, while clinically punishing their opponents at the other end.
Brazilian striker Joelinton has been criticised for a lack of goals since his £40m move from German club Hoffenheim but teed up Clark's opener with an unselfish header back across goal from Shelvey's free-kick and worked hard throughout.
Paraguayan winger Miguel Almiron was also lively for the visitors, only to be again let down by his end product and spurning a chance late on to score a fourth and ease the pressure.
Almiron has the pace to outsdtrip a defensive back line, but fails when he sees the whites of the goalkeeper's eyes. Meanwhile, Joelinton probably has the goalscoring touch, but he hasn't the pace to get himself inside the box!
Even though the opening two goals came from set-pieces, Newcastle constantly caused panic in the home defence through their pacy counter-attacking and should have enjoyed a greater margin of victory at London Stadium.
French youngster Allan Saint-Maximin was a particular nuisance throughout, causing veteran Hammers full-back Pablo Zabaleta all sorts of problems with his speed and trickery.
Saint-Maximin, 22, started to stretch the home defence and twice could have extended the lead when he sprinted through on goal only to be denied by Hammers keeper Roberto on both occasions.