Giroud - an early substitute for the injured Tammy Abraham - swept home the opener in the capital before the dangerous Werner stabbed home a second on the half hour.
It left Newcastle with too much to do after the break, and were unable to follow up last weekend’s 3-2 win over Southampton with a similar triumph against Thomas Tuchel’s improving side.
Chelsea started with intent, and created three openings inside ten minutes. Karl Darlow reacted well to keep out Marcos Alonso’s cross-shot, before a similarly important intervention from Dwight Gayle prevented Cesar Azpilicueta’s header from finding the target.
By the time Abraham glanced a header wide, Tuchel’s men seemed to be in control. Werner, who was growing in influence, slid a chance wide, but the German saved his more decisive input for a few minutes later. It was his run down the left which created Giroud’s opener; Darlow got a touch to Werner’s low cross to divert it away from Mason Mount, but the Frenchman was well-placed to fire home.
Werner then hooked a snapshot over the bar after a flowing move but with seven minutes left until the break, he got himself on the scoresheet. It was a scrappy goal but the frontman was able to profit from a fortuitous deflection off Jamaal Lascelles as the hosts attacked a corner, just about prodding it over the line despite Darlow’s valiant efforts to claw the ball to safety.
It was a difficult half for the Magpies, with few opportunities for Gayle - who replaced the injured Callum Wilson - to sniff out a goal which would have brought Steve Bruce’s men back into the contest. It was largely a similar story after the restart, although Jonjo Shelvey did force a good save from Kepa Arrizabalaga with a curling free kick from long range.
Joe Willock did pull a half-chance wide of the target after Allan Saint-Maximin had cut the ball back to him in the box, but in truth that was the closest Newcastle came. Callum Hudson-Odoi saw a shot deflected wide at the other end and Mateo Kovacic blasted over, while Alonso headed straight at Darlow.
But clear chances weren’t quite as forthcoming in what was a relatively low-key second half. Joelinton and Ryan Fraser were both deployed from the bench as Bruce sought a response, but the closest they came in the closing stages was a header from Willock. Arrizabalaga got down well to keep it out, though, rounding off a miserable evening for United.
