Two goals from midfielder Kevin Nolan and another from Joey Barton ensured a third 6-0 victory of the weekend following Chelsea's win over Wigan Athletic and Arsenal's thumping win over Blackpool.
Last season's runners-up Manchester United were held 2-2 at Craven Cottage after a frantic finish in which Fulham defender Brede Hangeland scored late on at both ends, after a Paul Scholes strike had earlier been cancelled out by Simon Davies for the hosts.
Carroll, the England under-21 international striker, staked his claim for inclusion in manager Fabio Capello's plans for the senior side with an outstanding performance to the delight of the watching Tyneside scoring hero Alan Shearer in the stands.
Barton fired home an angled shot after 12 minutes before Nolan headed in at the second attempt just after the half hour mark and Carroll made it three for the Magpies minutes later.
Carroll blasted in the fourth on 67 minutes with another Nolan header and a neat stoppage-time finish from Carroll sealing Newcastle's first points of the season. In an entertaining game at Craven Cottage, Scholes continued his fine form by giving United the lead on 11 minutes with a sweet low drive from 20 metres but Fulham levelled after the break when good work from Damien Duff and Bobby Zamora allowed Davies to thump home from inside the box.
United looked to have snatched victory on 84 minutes when Hangeland put through his own net but after Nani had a penalty saved soon after for the visitors, Hangeland rose highest to head home a stoppage time equaliser.
Earlier on Saturday, Nicolas Anelka and Salomon Kalou netted twice as Chelsea, who opened the season with a 6-0 win over West Bromwich Albion last week, crushed Wigan Athletic by the same margin.
Though Chelsea trounced Wigan 8-0 in May they had lost the away fixture to Roberto Martinez's team earlier in the season and they also looked second-best for the opening half hour on Saturday.
However, when Florent Malouda tapped in the rebound after keeper Chris Kirkland blocked a 34th-minute Frank Lampard shot, everything changed.
