Werner netted late in the first half at Stamford Bridge after setting up Olivier Giroud's opener for Thomas Tuchel's revitalised team.
It was a cathartic moment for Werner, who had gone 14 league games without a goal since scoring against Sheffield United in November.
The 24-year-old's only goal in his previous 19 matches in all competitions had come against minnows Morecambe in the FA Cup.
Werner was heralded as one of the best young strikers in Europe after his £50 million ($69 million) move from Leipzig in the close-season.
That hype has seemed misplaced during a difficult first season in England, but his 10th goal for Chelsea capped a lively performance that hinted at better things to come.
Tuchel is yet to lose in six games since replacing the sacked Frank Lampard in January, with five successive victories in all competitions suggesting the former Paris Saint-Germain boss could prove a shrewd appointment.
Chelsea are back in the Champions League places -- the minimum requirement for a Blues boss -- after climbing above West Ham on goal difference.
Tuchel is also two points above his fellow German Jurgen Klopp, whose troubled champions Liverpool are languishing in sixth place.
Fourth bottom Newcastle are seven points above the relegation zone, with third bottom Fulham holding a game in hand.
Marcos Alonso has benefitted from a clean slate since Tuchel took charge, displacing Ben Chilwell at left-back and the Spaniard threatened an early goal when his shot was well saved by Karl Darlow.
Cesar Azpilicueta went even closer as his header beat Darlow but was nodded off the line by Dwight Gayle.
Werner relief
Abraham was replaced by Giroud after suffering an ankle injury in a challenge with Jamaal Lascelles.
Werner was inches away from scoring when he stretched to reach Alonso's header, but the German's toe-poked effort drifted just wide.
Showing signs of emerging from his slump, Werner provided the assist for Giroud's 31st minute opener.
Moments after needing treatment for a cut lip, Werner whizzed past Emil Krafth with a clever shimmy and sent a low cross into the Newcastle area.
Darlow could only push it out to Giroud and the French striker lashed home from 10 yards for his first goal in six games.
With Chelsea well on top, Werner finally got back on the scoresheet in the 39th minute.
Mason Mount's corner was flicked onto the far post and Werner just about scrambled it into the net from close-range, with his wait to celebrate delayed just a few seconds longer while VAR ruled there was no handball by Giroud before the goal.
After exactly 1000 minutes and 31 shots, Werner had a smile on his face at last.
Mount should have killed off Newcastle before half-time, but the midfielder twice failed to hit the target from good positions.
Chelsea keeper Kepa Arrizabalaga was preferred to Edouard Mendy as the much-maligned Spaniard made only his fourth league start this season and his first since October.
Kepa repaid Tuchel's faith with a good stop from Jonjo Shelvey's free-kick in the second half.
Despite their revival under Tuchel, Chelsea are not the finished article and Newcastle exposed a few flaws in their defence, only to find the error-prone Kepa in unusually obdurate form.
Joe Willock flicked just wide from close-range, then drew a fine save from Kepa, who dived to his left to keep out the on-loan Arsenal midfielder's header.
smg/bsp