Maurizio Sarri named the striker, who signed on loan from Juventus in midweek, in his starting XI but the new arrival had minimal impact as the holders saw off their Championship opponents at Stamford Bridge on Sunday.
The Argentina international passed up the opportunity to make it a goalscoring bow, refusing Willian's offer of taking the 26th-minute penalty that the Brazilian subsequently tucked away for his 50th Chelsea goal.
In the build-up to the game, Callum Hudson-Odoi had reportedly handed in a transfer request amid interest from Bayern Munich but Sarri's selection was vindicated as the winger netted a fine second shortly after the hour.
Higuain was replaced by Olivier Giroud in the 82nd minute and the substitute swiftly had a hand in the third, laying the ball off for Willian to stroke home from the edge of the box and complete a convincing victory, three days on from the shoot-out win over Tottenham that earned Chelsea a place in the EFL Cup final.
It was Higuain who had the first sight of goal, firing wide on the turn following a cute pass from Mateo Kovacic, before VAR correctly overturned Andre Marriner's initial decision to award Wednesday a spot-kick when replays showed Ethan Ampadu won the ball ahead of Joey Pelupessy.
To make matters worse for the Owls, they soon conceded a penalty as ex-Chelsea midfielder Sam Hutchinson trod on Cesar Azpilicueta and Willian converted from 12 yards, sending Keiren Westwood the wrong way.
Wednesday came close to an equaliser early in the second period when Adam Reach's mis-hit cross clipped the outside of the post but it was a rare moment of optimism for the visitors as Higuain headed a half-chance wide from Ampadu's delivery.
The second did soon arrive, however, as Andreas Christensen lofted a ball over the top for Hudson-Odoi, who showed superb control before cutting inside left-back Morgan Fox with a classy backheel and firing beyond Westwood.
Wednesday's goalkeeper will perhaps feel he could have done better with that effort, but he could do nothing about Willian's precise finish as the Brazilian curled into the bottom-right corner after exchanging passes with Giroud.
What does it mean? Holders in the hat
Hudson-Odoi shows his class
It is not hard to see why Bayern are so keen to bring the teenager to the Bundesliga. He was lively all game and his marvellous touch, flick and finish was comfortably the highlight of an otherwise low-key affair.
Higuain on the periphery
Barring a couple of half-chances, Chelsea's new signing was not heavily involved on his debut before he made way for Giroud. With the Blues set to be involved in a tight tussle for Champions League places, Sarri will hope Higuain adapts quickly to his new surroundings.
Key Opta Facts:
- Chelsea have lost just one of their last 38 home FA Cup matches (W32 D5), with that coming against Bradford in 2014-15.
- Sheffield Wednesday have not won any of their last 20 FA Cup games against Premier League opponents (D6 L14), since beating Sheffield United in the 1992-93 semi-final.
- Sheffield Wednesday had the first shot on target in this match after just 72 seconds, but did not manage another one in the entire game.
- Chelsea scored with all three of their shots on target in this match.
- Willian scored his 50th and 51st goals in all competitions for Chelsea. 10 of his strikes for the Blues have come in the FA Cup, more than any other player for the club in that time.
- Callum Hudson-Odoi has been directly involved in five goals in his last five starts for Chelsea in all competitions (2 goals, 3 assists).
Chelsea resume league action with a trip to Bournemouth on Wednesday, while new Owls boss Steve Bruce will take charge of his side for the first time next weekend at the Championship's bottom club Ipswich Town.