Blues right-back Jose Bosingwa opened up the day's scoring in sensational style with his first goal in three years coming from a powerful 25-yard strike after picking up the ball in midfield.
Just after the hour-mark, Norwich managed to equalise through skipper Grant Holt's first Premier League goal which came about when Branislav Ivanovic and Hilario were tangled as they tried to deal with a long cross from the right.
As the pair fell to the ground, the ball popped up right next to Holt who used quick-thinking to scoop the ball over his left shoulder with his right foot into an open goal from the edge of the area.
Almost immediately down the other end, play was stopped for close to ten minutes when Didier Drogba was knocked unconscious in an aerial challenge with Canaries keeper John Ruddy before slamming into the turf as he fell from a decent height.
The Ivorian striker required oxygen as well as a stretcher as he was brought off the ground to a rapturous applause from all present at the Southwest London venue.
During the interval, new Blues signing Juan Mata snuck on as a second-half sub as Florent Malouda made way with Nicolas Anelka replacing Drogba as Andre Villas-Boas searched for a win. Teenage strike sensation Romelu Lukaku also made his Blues bow, coming on for Fernando Torres.
The home side then took the lead in dramatic fashion when a spirited Canaries outfit received a second debatable red card in two matches. Goalkeeper John Ruddy was given his marching orders with ten minutes remaining when he brought down Ramires in the area but it was a poor call from referee Mike Jones, who was right to award the penalty but not eject Ruddy, as the gloveman was not denying the Brazilian a goalscoring chance.
However, the red was brandished and Norwich had to bring on 20-year old Declan Rudd for his Premier League debut only to see Frank Lampard step up and hammer the spot-kick straight past and down the middle to make it 2-1.
In a match full of scoring chances, three goals total would have been a waste but luckily for Chelsea fans, they were treated to a debut goal from £26million signing Mata who pounced on a defensive error from Ritchie De Laet to calmly slot past Rudd to end it, in the 11th minute of stoppage time, at 3-1.
Chelsea now have two wins and a draw from their opening three matches whilst Paul Lambert's Norwich have two draws so far in their top flight return.
Red card:NOR - John Ruddy 80'