A Willian brace, and a well-taken goal from Callum Hudson-Odoi, secured a second consecutive cup victory in a matter of days and booked our passage through to the FA Cup fifth round.
It was a comfortable evening's work for Maurizio Sarri's side, with the result never in doubt from the moment Willian converted a first-half penalty with what was his 50th goal for the club after VAR had been consulted.
That came just moments after VAR had overturned the decision to award the visitors a spot-kick following a challenge by Ethan Ampadu on Adam Reach, but it was clear in both cases the final decision was the correct one.
Hudson-Odoi made it 2-0 after the break with a left-footed drive after being well found by Andreas Christensen, before Willian capped a fine individual display with his second goal of the night late on, exchanging passes with Olivier Giroud before curling home.
Midweek arrival Gonzalo Higuain was put straight into the starting line-up by Sarri in one of eight changes to the side which beat Tottenham in the Carabao Cup, with only Cesar Azpilicueta, Toni Rudiger and Ross Barkley retaining their places.
There was a start for Willy Caballero while Marcos Alonso, a sub on Thursday, came in at left-back. With Jorginho on the bench, Ampadu was deployed as the deepest of the midfield trio, while Willian and Hudson-Odoi supplied the width in attack.
N’Golo Kante and Eden Hazard were not part of the matchday squad, although there was a place on the bench for Ruben Loftus-Cheek, who hadn’t featured since the third-round win over Nottingham Forest due to injury.
It was the visitors who had the first sight of goal as Reach picked up possession deep inside the Chelsea half and burst towards goal, with the midfielder’s angled strike deflecting safely into the arms of Caballero.
The Blues were seeing plenty of the ball during the opening stages but with Sheffield Wednesday keeping their shape defensively, our first attempt was a strike from distance by Ampadu which flashed just wide.
The sharp and clever movement of Higuain led to an opportunity just before the 20-minute mark as the striker raced on to a Mateo Kovacic pass inside the box, but as he spun and fired towards goal the strike was deflected behind, although bizarrely no corner was given.
Just moments later, however, the first of two controversial moments in quick succession arrived as Reach exchanged passes with Steven Fletcher and advanced into the box before going down after being challenged by Ampadu.
The Chelsea midfielder, at first glance, appeared to have won the ball fairly, but the referee immediately pointed to the spot. However, after consulting VAR, the initial decision was overturned, much to the frustration of the travelling Wednesday fans packed into the Shed End.
Our next attack led to the opening goal of the game but, once again, VAR was required after former Blue Sam Hutchinson stepped on the foot of Azpilicueta as he collected a pass from Hudson-Odoi inside the penalty area. On this occasion the spot-kick was awarded, and rightly so.
Willian, a scorer in Thursday’s successful shoot-out against Tottenham, stepped forward and made no mistake, sending Wednesday keeper Keiren Westwood the wrong way to make it 1-0.
The Blues continued to dominate in terms of possession, looking to utilise the pace and directness of Willian and Hudson-Odoi in wide areas, but clear-cut opportunities were proving hard to come by and as the teams headed in at the break, they were only separated by Willian’s penalty.
Six minutes into the second half Caballero was almost caught out by a hopeful Reach cross from the right-hand side, which bounced back off the outside of the post, and at the other end Alonso was unable to convert a teasing Willian cross after the Brazilian had got the better of Liam Palmer with a wonderful piece of skill.
As Sarri’s side went in search of a second goal Higuain glanced a header wide from Ampadu’s delivery, but we wouldn’t have to wait long for an extension of our advantage, and it came from the boot of Hudson-Odoi.
The attacker was picked out by Christensen, who delivered an inch-perfect ball from deep. Hudson-Odoi still had plenty to do, but after cutting inside Morgan Fox with a clever flick, his left-footed strike beat Westwood for power and crept in at the near post.
It was his second goal for the club and one which provided us with a healthy cushion midway through the second half.
Loftus-Cheek made his return from injury soon after and replaced Ampadu, with Kovacic dropping back into a deeper midfield role.
With 10 minutes remaining a solid first outing for Higuain came to an end as the striker was replaced by Giroud, and the Frenchman's impact was immediate as he cushioned a pass from Willian back into the Brazilian's path for him to curl a delightful strike into the bottom corner, all but finishing the game as a contest.
Giroud almost put the seal on the victory in the last few minutes with an audacious acrobatic volley from a lofted Jorginho pass, only to see his effort fly just wide of the post, but the damage had already been done.
All in all, it was a positive afternoon for the Blues with Higuain playing all but the last 10 minutes and Loftus-Cheek returning from injury.
Most importantly, however, we're safely through to the fifth round, and we wait to find out who we will play when the draw is made tomorrow night.
Chelsea (4-3-3): Caballero; Azpilicueta (c), Christensen, Rudiger, Alonso; Barkley (Jorginho 84), Ampadu (Loftus-Cheek 65), Kovacic; Hudson-Odoi, Higuain (Giroud 80), Willian.
Unused subs: Kepa, David Luiz, Emerson, Pedro,
Scorers Willian (pen) 26 and 83, Hudson-Odoi 64
Sheffield Wednesday (4-5-1): Westwood; Palmer, Lees (c), Thorniley, Fox; Reach, Pelupessy (Forestieri 68), Hutchinson, Bannan, Boyd (Joao 75) Fletcher (Nuhiu 75).
Unused subs: Dawson, Baker, Pudil, Matias
Booked Fox 38
Referee Andre Marriner