Jon Gorenc Stankovic - making his first appearance in 17 months due to a knee injury sustained at this ground - netted Huddersfield's consolation goal, but David Wagner's team face the prospect of a tough second season among English football's elite.
City wasted no time in showing their attacking intent, but it was Huddersfield's Steve Mounie who almost gave the home side the lead with the forward slicing a clearance onto the top of his own crossbar.
Jesus was then denied twice by goalkeeper Ben Hamer - the second effort coming from no more than four yards out - but it appeared that Huddersfield had weathered the storm when Gorenc Stankovic fired over at the other end of the pitch.
However, from the resulting goal kick, Ederson fired a long pass to Aguero and after the Argentine had remained patient as he found a shooting position for himself, the ball was clipped over Hamer and a defender before finding the top corner of the net.
City added a second six minutes later through Jesus, who was perfectly placed to drill a shot into the bottom corner from 20 yards after Benjamin Mendy had been prevented from entering the penalty area.
A third goal arrived shortly afterwards as Aguero converted from close range, but it was Hamer's mistake which led to the striker converting from six yards after he had failed to claim a cross from Mendy.
City were already beginning to think about how many goals they could score against opponents who were offering nothing in the final third, but just before the break a long throw was flicked on by Mounie and Stankovic was able to reduce the deficit with a confident finish from close range.
Huddersfield needed to be able to take their momentum into the second half, but within three minutes of the restart City re-established their three-goal advantage as Silva curled a 25-yard free kick into the top corner of the net.
That strike enabled City to regain total control of the match and it led to a sustained period of possession, which was only broken up when Aguero sent a low shot from 20 yards off the inside of the post.
Aguero then fired wide from inside the penalty area after being teed up by Jesus, and Hamer had to come to the rescue to prevent the forward from finding the bottom corner.
However, it was only going to be a matter of time before Aguero netted his treble, with Mendy picking out the run of his teammate who flicked the ball into the far corner from six yards out.
The intensity of the game had been dropping, but City were still able to add a sixth goal before the full-time whistle when Kongolo diverted the ball into his own net after Hamer had saved Leroy Sane's close-range effort.
MANCHESTER CITY (3-4-3): Ederson; Stones, Kompany, Laporte; B.Silva, Gundogan (Foden 82'), Fernandinho, Mendy; D.Silva (Mahrez 64'), Jesus, Aguero (Sane 76')
HUDDERSFIELD TOWN (3-5-1-1-): Hamer; Schindler, Stankovic, Kongolo; Smith, Hadergonaj, Sabiri (Depoitre 46'), Billing, Lowe; Pritchard (Diakhaby 61'); Mounie (Sobhi 84')