The oft-maligned Werner - a £53million summer signing from RB Leipzig - had failed to score in his previous 12 appearances before tapping home on the stroke of half-time at Stamford Bridge on Sunday.
Chelsea already led their League Two opponents - 66 places below them in the football pyramid - through birthday boy Mason Mount’s excellent early strike, while Callum Hudson-Odoi and Havertz both netted in the second half to continue the hosts’ record of never failing to reach the fourth round this century.
Playing their first game since Boxing Day having only returned to training earlier this week following a Covid-19 shutdown, Morecambe - chasing the play-offs in the fourth tier after avoiding relegation last term - could have taken a shock early lead in west London.
Former Liverpool midfielder Adam Phillips’ swerving cross/shot was almost carried over his own goal line by Kepa Arrizabalaga, who then showed impressive agility on his 100th Chelsea appearance to stop the ball from going in.
Chelsea showed six changes from the Premier League defeat by Manchester City but Frank Lampard still named a strong squad in a bid to recover from a woeful run of only one win in seven matches - and four defeats in six - across all competitions that had led to speculation over his own future. Werner nodded wide in the opening minutes, while Antonio Rudiger and Havertz both had efforts blocked before Emerson Palmieri sliced well wide.
Hudson-Odoi also had a shot deflected over after Kepa’s scare and Rudiger wasted a good chance from a corner before Mount broke the deadlock.
The England midfielder received possession from Hudson-Odoi before rifling an effort from 25 yards and into the bottom corner. A fine goal - only his second of the season and first since September - to mark his 22nd birthday.
Rudiger went close again as Chelsea piled on the pressure, but Morecambe defended resiliently and Havertz’s rogue defensive header from a long throw into the six-yard box led to panic and saw Kepa have to palm the ball away from danger.
The Blues were dominant but did not create too many clear-cut chances, with Werner awkwardly volleying well over the top. Phillips tested Kepa again and Havertz failed to connect properly with a free header from a set-piece before Chelsea did double their advantage just before the break.
The impressive Hakim Ziyech’s inviting delivery to the back post was headed across goal by Havertz and Werner - without a goal to his name since November 7 - could not miss with his tap-in from only a couple of yards out.
Chelsea started the second half on the front foot and quickly extended their lead further, with Ziyech again the architect as his latest delivery was picked up by Hudson-Odoi, whose first touch was not the best but he put enough power on the shot to prevent Morecambe goalkeeper Mark Halstead from making the save.
Ziyech was full of confidence as he arrowed a dipping left-footed strike narrowly over the crossbar and Werner turned provider for Havertz after a Hudson-Odoi-led break, but the former Bayer Leverkusen man could only sweep a low shot wide.
It was attack against defence for the majority of the second period as Chelsea hunted a fourth and Morecambe were let down by sloppy passing on the very few occasions that they did manage to wrestle back possession.
A long ball from Rudiger was almost perfect for Ziyech, only for Nathaniel Knight-Percival - starting in place of Shrimps captain Sam Lavelle, who tested positive for Covid-19 last week - to do just enough.
Ziyech was content to try his luck from anywhere and Halstead made a stellar double save to deny both Havertz and substitute Christian Pulisic in quick succession.
Olivier Giroud also came off the bench and had a few late sights of goal for Chelsea, who did grab a fourth when Tammy Abraham combined well with Cesar Azpilicueta and the captain’s deep cross from the right was headed in by Havertz.
Morecambe’s only half-chance of note in the second half was a looping Harry Davis header that caused no issues for Kepa.