But the loudest cheer of the day was reserved for the returning Kevin De Bruyne who took only 17 minutes to claim his first assist of the season after more than four months out.
The Belgian playmaker set-up compatriot Jeremy Doku - who had also been out with injury for five weeks - to volley home the fifth of the game on 74 minutes.
Huddersfield Town may be fighting relegation in the Championship, but they made a bright and confident start against City.
And when the Blues had the ball, the visitors sat deep and in numbers, frustrating the hosts in the process.
A clumsy tackle by Alex Matos on 16 minutes ended Manuel Akanji’s afternoon, and City’s general passing and movement was far from its fluent best as the clock ticked past the half-hour mark with little incident.
Then, finally the Huddersfield defence was breached as a clever combination of short passes with Alvarez feeding the ball to Phil Foden on the corner of the six-yard box and his fierce angled shot gave keeper Lee Nicholls no chance.
Four minutes later and City had doubled that advantage with another move that picked apart the Terriers’ defence.
That was expertly prodded home by Alvarez for his 13th of the season to send the Blues in two goals to the good at the break.
City fans have waited a long time to see De Bruyne return to action after more than four months out and the reception he received when he came on after 57 minutes was both stirring and emotional.
Jeremy Doku was also welcomed back with open arms as he returned after a five-week absence.
Within a minute of that double substitution the Blues had wrapped up victory as Nunes found Bobb and his attempt at finding the unmarked De Bruyne took a mighty deflection to wrong-foot Nicholls and fly into the net.
And City were far from finished, with the Terriers visibly wilting under the constant pressure, the ball was played to the outstanding Foden who skipped past one challenge before fizzing a low shot into the bottom left corner from 20 yards.
However, the loudest celebration of the day was reserved for City’s fifth on 74 minutes as Bobb slipped the ball to De Bruyne and his looped chip into the middle was swept home by Doku - it had taken KDB just 17 minutes to register an assist!
EDS youngster Jacob Wright was handed his senior debut shortly after and though there were a couple more half-chances in the time that remained, City declared at five in what was an enjoyable afternoon’s work by the FA Cup holders who now go into the hat for the fourth round tomorrow evening.
HUDDERSFIELD TOWN XI: Nicholls, Edmonds-Green, Helik (C), Rudoni, Koroma (Diarra 81), Thomas, Spencer, Matos (Radulovic 61), Wiles (Iorpenda 88), Jackson, Lees
Subs: Bellagambi, Edwards, Hudlin, Austerfield, Ayina,, Stone
Man of the Match
Phil Foden‘s irresistible form continued against Huddersfield.
The City playmaker opened the scoring before playing an incisive pass in behind the visitors’ defence that led to the second goal shortly after.
He tracked Sorba Thomas’ run towards goal as the last man to win possession midway through the second-half before drilling home the Blues’ fourth on 65 minutes.
An all-action performance by a gifted footballer.
“Kevin played really good minutes, and we thought it was better in the second-half when there was more space because they defended really, really deep and the spaces were so hard to find,.
“But in the second half there were more spaces and we played with good intention, and it was really, really good.
“Now, as I said in the previous press conferences, Kevin needs to accumulate training sessions, training sessions and more training sessions – even more than games.
“Now with Newcastle (next weekend) we have another chance, then we have two weeks to have good training sessions here and in Abu Dhabi, so we are ready for the second part of the season.
“But I am incredibly happy to have him back because Kevin helps you to win games.”
made in belgium
What a fantastic sight to see De Bruyne back doing what he does best.
The Blues’ assist king looked sharp and full of energy after his appearance on 57 minutes - met by a standing ovation from a packed Etihad - and he was soon in the thick of the action.
He almost had a dream start as Bobb attempted to find his unmarked run into the box, but the ball instead deflected into the net.
He then fizzed a shot just over the crossbar before teeing up compatriot Doku - also making a welcome return - for City’s fifth.
It’s the first time the two Belgians have played together in sky blue and it took them only 17 minutes to combine for a well-taken goal.
It all bodes very well for the Blues and the many challenges that life ahead.
What it means...
City progress into the FA Cup fourth round after the victory over Huddersfield Town.
The draw for the last 32 will take place on Monday evening on ITV ahead of the Wigan Athletic v Manchester United third round tie.
City return to Premier League action next Saturday (13 January) with a tough-looking trip to face Newcastle United at St James’ Park.
The match will kick-off at 17:30 (UK), with the Blues looking to avenge a 1-0 Carabao Cup defeat on Tyneside back in September.
News about Man City v Huddersfield
Foden: We’re buzzing with KDB return
Phil Foden says the dressing room is thrilled with the return to action of Kevin De Bruyne. Read more
Pep's praise for 'incredible threat' Bobb
Pep Guardiola praised another fine afternoon’s work from Oscar Bobb, describing the attacking midfielder as an ‘incredible threat’ after City's comprehensive 5-0 FA Cup third round win against Huddersfield Town. Watch more
Dickov: Wonderful De Bruyne looked as if he had never been away!
Paul Dickov hailed Sunday’s long-awaited return to action of Kevin De Bruyne, describing the City playmaker’s instant impact against Huddersfield Town ‘as if he had never been away.’ Read more
Guardiola: ‘Our people are in love with Kevin'
Pep Guardiola says there is a mutual respect between the City fans and Kevin De Bruyne that will ‘last forever’. Read more
City 5-0 Huddersfield: Tunnel Cam
Go behind-the-scenes as City kicked off the New Year with a 5-0 victory over Huddersfield Town in the FA Cup. Watch more
Full-match replay: City v Huddersfield Town
Enjoy the full 90 minutes of City's FA Cup third round clash with Huddersfield Town on CITY+. Watch more
City 5-0 Huddersfield Town: Extended highlights
Watch the best moments from our FA Cup third round victory over Huddersfield Town at the Etihad Stadium. Watch more
City extend run of FA Cup fourth round appearances
City’s 5-0 victory over Huddersfield Town on Sunday means we have reached the fourth round of the FA Cup in each of the last 12 seasons. Read more
City 5-0 Huddersfield Town: Brief highlights
Watch the goals from our emphatic FA Cup third round victory over Huddersfield Town at the Etihad Stadium. Watch more
City 5-0 Huddersfield Town: Pitcam highlights
Watch City’s thrilling FA Cup third round victory over Huddersfield Town from a unique angle on CITY+. Watch more