Chelsea scored a hat-trick, Tammy Abraham in the third and 68 minutes, and Mason Mont in the 17th minute, while Norwich scored twice, Todd Cantwell in the sixth minute, and Timo Buckey in the 30th minute.
With this victory, Chelsea took the tally to 4 points in 10th place, while Norwich froze at 3 points in 13th place.
The game saw a strong start from both teams, with Chelsea scoring early in the third minute, after a counter-attack that reached the right side of César Azpilicueta, who sent a fine cross to Tammy Abraham, the latter hit the floor with a right foot against Tim Kroll.
Norwich City did not need more than three minutes, until the equalizer through Todd Cantwell, after a series of passes in the penalty area, ended with a pass from striker Timo Buckey to Cantwell, who scored against goalkeeper Kepa.
The Blues scored the second goal quickly, in the 17th minute through Mason Mont, where Christian Pulisic passed a magic ball to the young Englishman, who broke through the penalty area and dribbled before he hit hard in the net.
Chelsea almost scored the third goal in the 25th minute, after a powerful header from defender Christensen, but Kroll was saved by brilliantly.
Norwich City leveled the score in the 30th minute, after Emiliano Buendia passes from Finnish striker Timo Buckey, behind defender Kurt Zuma, where he was alone with Kepa from the right side, firing a ball that touched the fingers of the Spanish goalkeeper, before netting.
Chelsea dominated the game in the first 15 minutes of the second half.
The 68th minute saw Norwich’s first danger, with the team’s top scorer Buckey, who fired a powerful ball from the left side of the penalty area, Kepa was saved.
Abraham scored his second goal of the game, and the third for Chelsea, in the 68th minute, after receiving a long pass from Kovacic, to start and aim a perfect ball from outside the penalty area against Kroll.
Norwich sought to equalize for the third time, from a corner raised defender Ben Godfrey in the 72nd minute, to hit a header hit the crossbar.
Referee Martin Atkinson canceled a goal for Chelsea in the 78th minute through Zuma, following a foul from Giro with goalkeeper Kroll.
Barclay almost scored the fourth goal, in the second minute of stoppage time, as he headed towards a defensive ball into a corner, before the game ended with a precious victory for Chelsea (3-2).