The Blues got back on track with a much-needed victory on Saturday as Andre Villas-Boas' men leapfrogged the Magpies into the top four.
Drogba's third goal of the season was the platform for a victory sealed by late goals from Kalou and Sturridge.
Magpies keeper Tim Krul pulled off a string of fine saves, including one from Frank Lampard's 14th-minute penalty, to keep the visitors at bay before the late flurry, but the home side were denied by the woodwork on three separate occasions.
Victory will have come as a relief to under-pressure Villas-Boas, who had seen his side lose three of their last four games, while opposite number Alan Pardew could once again be proud of a team which started the game without Cheik Tiote and Leon Best and lost central defenders Fabricio Coloccini and Steven Taylor before the end of it.
If Lady Luck smiled on Newcastle in the draw at Old Trafford last weekend, when they were awarded the most dubious of penalties, she turned her back on them this time around.
There were just four minutes gone when Yohan Cabaye slid the ball in behind David Luiz to put Demba Ba in on goal. The Brazilian's response was to cynically haul down the striker a yard or two outside the penalty area with only keeper Petr Cech standing between him and the opening goal.
Referee Mike Dean took his time to make up his mind, but then, inexplicably in the eyes of the bulk of a crowd of 52,305, produced only a yellow card.
It was an issue Pardew no doubt sought to address when he met the official as he left the pitch at half-time with his team trailing 1-0, although the scoreline could have been markedly different.
The Newcastle boss had attempted to counteract Chelsea's 4-3-3 formation by playing Peter Lovenkrands in an advanced role on the left hand side with the usual occupant, Jonas Gutierrez, suspended.
But all the ploy achieved was to highlight how much protection the Argentinian gives full-back Ryan Taylor, who found himself repeatedly exposed to the pace of Sturridge.
The fledgling England international needed no second invitation as he tore into the Magpies, and had it not been for the excellence of Krul, the visitors might have ben out of sight by the break.
It was he who lured Cabaye into an injudicious 13th-minute challenge inside the penalty area which gave Mr Dean little choice but to point to the spot, although Krul dived to his left to turn Lampard's effort on to the post.
The same upright came to Krul's rescue two minutes later when Sturridge rattled it with a rising drive, and he twice denied the striker one-on-one as Chelsea attacked in waves.
They eventually took the lead seven minutes before the break when Cabaye switched off long enough to allow Mata to collect Ashley Cole's throw-in and cross for Drogba to head home.
Despite being good value for their advantage, the visitors had come under some pressure, and Cech had to pull off a fine reaction save to keep out Ba's audacious 24th-minute flick from Lovenkrands' cross.
The Senegal international was unfortunate to see a 35th-minute header come back off the post, and John Terry was relieved to see his attempted clearance drop wide of the goal after blasting the ball straight at team-mate Luiz.
Lovenkrands found himself playing as an orthodox left-sided midfielder after the break when Pardew replaced Hatem Ben Arfa with striker Shola Ameobi and adopted a 4-4-2 formation.
They immediately looked a greater threat, although they might have fallen further behind seven minutes after the restart when Drogba chested down Branislav Ivanovic's cross at the far post, but fired wide.
The Chelsea striker hit the bar with 55 minutes gone, but he did so at the wrong end as he beat Ba to Cabaye's corner, and Ramires was denied by Krul as the visitors counter-attacked at lightning pace from the rebound.
Ameobi shot just wide from distance in an increasingly open encounter with the home side gearing up for a big push.
Younger brother Sammy Ameobi was denied a 74th-minute equaliser when Terry cleared his volley off the line, and Shola saw his piledriver come back of the bar with Cech helpless six minutes later.
But with Steven Taylor having to leave the pitch injured, Kalou struck from close range in the final minutes of normal time and Sturridge made it three in stoppage time to give the scoreline a slightly flattering appearance.