While City close the gap between themselves and second-placed Leicester City to four points, Arsenal remain in ninth position, seven points adrift of Chelsea who fill the last top-four spot.
The afternoon could have turned out differently for Freddie Ljungberg's team as Gabriel Martinelli almost opening the scoring within the first 60 seconds, only for Ederson to make a smart stop at his near post.
However, after receiving a pass from Gabriel Jesus, De Bruyne set City on their way with a sublime first-time effort into the roof of the net from just inside the penalty area.
Arsenal were offering a threat at the other end through the lively Martinelli and Nicolas Pepe, but it was not long before De Bruyne went from goalscorer to provider.
The playmaker broke down the left-hand side before firing a low pass across the penalty area for Sterling, who had the relatively simple task of converting from six yards out.
Despite less than a quarter of the match being played, it felt over as a contest, with De Bruyne constantly finding himself in space in threatening areas.
An injury to Sead Kolasinac contributed to a lull in the action shortly after the half-hour mark, and the Gunners would have been hoping to reach half time facing just a two-goal deficit.
However, before the enforced alteration could be made, City went further in front as De Bruyne turned away from Matteo Guendouzi before curling a sublime effort into the bottom corner from 20 yards.
Within minutes of that goal, the Belgium international almost completed his hat-trick in some style, only for Bernd Leno to pull off one of the saves of the season to tip his first-time strike, seemingly destined for the top corner, onto the left-hand post.
Ljungberg resisted the temptation to make changes at half time, and the show of faith almost paid off as Pierre-Emerick Aubameyang sent a glancing header just wide of the far post.
City almost extended their advantage soon afterwards, however, with Jesus tamely firing over from the edge of the area when he should have at least tested Leno.
While both managers made alterations during the middle of the half, it did not increase the urgency from either side, a sign that the end result had already been accepted.
As Arsenal's fans made their way to the exits, City enjoyed a sustained spell of possession before pushing for a fourth, with Riyad Mahrez being denied by Leno at his near post.
Sterling also narrowly missed the far post as Guardiola demanded a strong finish from his team, but the Spaniard will be more than satisfied with a convincing triumph and performance against a team who had regained some belief earlier in the week.
ARSENAL (4-2-3-1): Leno; Maitland-Niles, Chambers, Sokratis, Kolasinac (Saka 40'); Torreira (Willock 81'), Guendouzi; Pepe, Ozil (Smith Rowe 59'), Martinelli; Aubameyang
MANCHESTER CITY (4-3-3): Ederson; Walker, Otamendi, Fernandinho, Mendy (Zinchenko 85'); Gundogan (Mahrez 70'), Rodri, Foden (B.Silva 56'); De Bruyne, Jesus, Sterling body check tags ::