The result gives Frank Lampard his first win as Chelsea manager after losing to Manchester United and drawing with Leicester City in his opening two games.
Norwich’s Teemu Pukki scored once again as he registered his fifth league goal of the season but it was not enough to earn the home side a point.
Frank Lampard selected Tammy Abraham ahead of Olivier Giroud to spearhead Chelsea’s attack and the Englishman repaid his manager’s faith by sweeping in Cesar Azpilicueta’s cross as early as the third minute to give the visitors the lead.
Just three minutes later Norwich found the equalizer as Todd Cantwell latched onto Teemu Pukki’s pass to finish through Kepa’s legs.
Chelsea retook the lead in the 17th minute as Pulisic’s pass found Mason Mount, who cut inside the Norwich defenders and fired an unstoppable shot past Tim Krul in the Norwich goal.
Krul came to Norwich’s rescue ten minutes later as he tipped Andreas Christensen’s point-blank header over the bar.
Teemu Pukki continued his explosive start to the season by drawing Norwich level for a second time in the 30th minute, when he fired an angled shot past Kepa after being played through by Emiliano Buendia.
Chelsea edged ahead for a third time after the break through Tammy Abraham once again, as he did well to stay onside before outwitting two Norwich defenders to fire a low drive past Krul in the 68th minute.
Norwich threatened another equalizer but Ben Godfery’s header from a corner came off the crossbar and landed safely into the hands of Kepa in the 72nd minute.
