Hoffenheim's 2-2 draw with Lyon in the night’s other Group F game means City still haven't officially confirmed our place in the knockout stages.
But given this sort of irresistible form. City will be confident of seeing the job through in our final two group games.
It proved to be a memorable night for Jesus who claimed his first-ever hat-trick in senior football with David Silva, Raheem Sterling and Riyad Mahrez also on target to secure a back-to-back double over the Ukrainians and the Club's biggest margin of victory in the Champions League.
In contrast to our whirlwind start against Southampton, it took a while for the Blues to find their fluidity and rhythm with Shakhtar proving obdurate opponents in the early stages and having the first shot on goal through Moraes’ tame effort.
But all that changed in the 13th minute when City opened Shakhtar up in simple but devastating fashion.
Riyad Mahrez, deployed on the right wing, was the architect, twisting and turning the Donetsk back-line before unleashing a defence-splitting cross which found skipper David Silva unmarked in the box.
El Mago needed no second invitation to side foot the ball home for his third goal in as many Champions League matches to provide the ideal start.
It was a significant strike in many ways – not least the fact it saw Silva overtake Francis Lee on our all-time European goal-scoring record with the Spaniard now having notched up 11 over the course of his illustrious City career.
Within 10 minutes City had doubled our advantage, though this time in slightly fortuitous circumstances.
Clean through on goal, Raheem Sterling came down and Hungarian referee Viktor Kassai awarded a spot-kick.
Gabriel Jesus made no mistake from the spot, coolly beating Donetsk keeper Andriy Pyatov to double City’s lead.
However, TV replays indicated that Sterling had actually tripped after kicking the ground before Mykola Matviyenko, who was subsequently booked, could make a challenge.
Within minutes Jesus had almost made it three after a sumptuous Sterling through-ball but the striker drilled his shot straight at Pyatov.
Impressive Donetsk skipper Taison looked to carry the fight to the Blues but it was a forlorn task with City simply a class apart.
That was reinforced four minutes after the restart by a quite wonderful goal from Sterling.
Picking up the ball midway in the Shakhtar half, the England man drifted inside two defenders before curling a stunning effort inside the right-hand post.
It was a breath-taking moment that further reinforced how Raheem has lifted his game to a new elevated level this season.
In complete control, City were awarded a second penalty on 70 minutes - and this time there was no debate as David Silva was hacked down in the box.
Jesus duly dispatched his second spot-kick of the night with aplomb to further illustrate the Blues' all-round supremacy.
There was even time for Ederson to keep his hands warm with a stupendous diving save to keep out Kovalenko's free-kick.
It was high fives all-round when Mahrez deftly brought the ball under control before drilling home an 84th minute effort.
And Jesus set the seal on a fine night's work by sealing his hat-trick in injury time with an exquisite chip.
Man of the match
Gabriel Jesus - His hat-trick was just reward for another fine all-round display from the Brazilian.
Pep Guardiola spoke last week of how happy he was with Jesus's all-round contribution - but this three-goal return will fill the player with extra confidence and belief.
As Pep said, striker's live to score!!
What it means
City are top of Group F on nine points, three clear of Lyon and six clear of Hoffenheim with two games remaining in the group stages.
Next up in in Europe is a trip to Lyon later this month before we round off the group stages in December at home to Hoffenheim.
“I am really happy. We did again an incredible performance. The way we attack, the way we defend.
“The only problem is if we believe it is easy, it is not.
“It is unfortunate we are not qualified but we area so close.
“We need to keep and maintain that level.
"The quality of Gabriel is that he always fights. It is important for him to score goals for his confidence and for the team."
City round off a hectic run of four games in 10 days with the biggest of them all.. Sunday’s Manchester derby with United here at the Etihad.
The Blues will go into the game two points clear at the top of the Premier League and a fourth successive league win would send Pep’s side into the international break in great heart.