The Blues had narrowly beaten Newcastle at Stamford Bridge in the Premier League three days earlier but United gained some revenge by knocking them out of the cup thanks to Alexander Isak's third goal of the campaign and a Axel Disasi own goal.
Enzo Maresca named an entirely different starting XI to Sunday, while Howe made five changes - including the return of Anthony Gordon after he missed out in the capital with a groin injury.
And the home side started confidently, fashioning a big opportunity to open the scoring in only the second minute as Isak drilled a great ball in from the right and Joelinton's shot hit the base of a post.
In the eighth minute, Sandro Tonali made an important block to keep out Renato Veiga's seemingly goalbound effort, then João Félix seized possession in midfield and jinked towards the edge of the box but fired over.
However, Newcastle's press was making it difficult for Chelsea to play out from the back, as they look to do under Maresca, and in the 23rd minute the Magpies capitalised.
Joelinton and Tonali worked in tandem to win the ball and the latter slid in to divert it into the path of Isak, who swept home his second goal against Chelsea in the space of four days.
Two minutes later, more fantastic work from Joelinton saw him lay the ball off for Tonali, whose 20-yard strike whistled agonisingly wide.
But it was 2-0 in the 27th minute, when Lewis Hall - facing his former side - slid a quick, clever free kick to Isak, who had peeled away from the Chelsea defence on the left hand side. The Swede's cross took a deflection in its way towards Joe Willock but he adjusted to connect with a firm header, which may well have been going over the line before Disasi inadvertently ensure that it did.
Willock was involved once more in the 31st minute when teed up by the outstanding Tonali, but he scuffed his shot from outside the box and it went wide.
Lloyd Kelly made an outstanding block to thwart Félix before the the Portuguese playmaker saw a dipping shot pushed away from danger by Nick Pope.
Two minutes later, the Newcastle netminder made another smart save from Félix, diving to his right to keep out a snapshot from Christopher Nkunku's pass.
In first-half stoppage time, United threatened to kill the match off as Gordon streaked down the right and crossed but Willock - at full stretch - couldn't find the target.
Chelsea were much improved in the second half, and Kelly made a vital block from Nkunku in the 50th minute before the home side broke and worked the ball to Hall, whose low shot was saved by Filip Jörgensen.
But despite the visitors' dominance, they failed to find a way past the United backline - although perhaps should have halved the deficit when Félix latched onto a threaded pass from Tosin Adarabioyo but prodded wide with just Pope to beat.
Indeed the Magpies were the team to find the net again when Sean Longstaff - on his 27th birthday - forced home at the Gallowgate End, but his celebrations were cut short by an offside flag.
Substitute William Osula was then unfortunate in the 84th minute to see his strike hit the woodwork after he had made space brilliantly - but United deservedly went through to the last eight after Pope parried Veiga's shot in the last minute of normal time.
