Goals from Fernandinho, Kevin De Bruyne, and Sergio Aguero were more than enough to see off Albion and allow City open up a 15-point gap in their relentless march towards the title — with just 13 games remaining.
After pulling out of a proposed move for Leicester winger Mahrez earlier in the day, after his club rejected City’s offer of £65m (€75m), Guardiola’s team still managed to field one debutant in what looked like being a perfunctory stroll against Albion, right from kick-off.
French centre-half Aymeric Laporte, signed from Athletic Bilbao for a club record £57m just 24 hours earlier, took the place of John Stones, ruled out with sickness.
If Guardiola’s logic was that the 23-year-old would not be too severely tested by the league’s bottom team, he was quickly proven correct.
It took City 19 minutes to take the lead, through Fernandinho, although their perfectionist manager would have been displeased with the sheer volume of first-half chances they wasted.
The goal, predictably, was suitably impressive as De Bruyne played a long pass which allowed Fernandinho to slip goal side of Gareth McAuley before clinically beating Ben Foster from the corner of the six-yard area.
The chances and dominance soon mounted. Minutes later, David Silva centred but Aguero hesitated, Then De Bruyne, of all people, was guilty of a rare error when an Aguero flick played him clean through but the midfielder shot directly at Foster.
City goalkeeper Ederson was not required to touch the ball with his hands in the opening half.
But there was a fleeting moment of concern for Guardiola when David Silva was forced out of the action on 39 minutes, walking with what looked like a lower back injury.
His replacement, German international Ilkay Gundogan, helped set up an early second-half chance from which Raheem Sterling should have settled the outcome but he curled wide.
Aguero might have doubled the tally with a marvellous piece of improvisation, back-heeling a Bernardo Silva cross from six yards out but finding Foster alert to the danger.
Then Gundogan picked out Bernardo Silva who switched the ball onto his left foot on the edge of the area and produced a shot which Foster parried acrobatically.
City scored their second on the counter attack, as Gundogan led the charge after a rare Albion attack broke down.
De Bruyne took the ball on, being fouled by James McClean but continuing, exchanging passes with Raheem Sterling and converting impressively into the right-hand corner from a dozen yards.
De Bruyne was obviously inspired by McClean’s crude lunge — one which, correctly, earned him a booking — and moments later attempted an audacious chip from just inside the Albion half which had Foster back-pedalling furiously and tipping the ball over for a corner.
Kyle Walker was soon in on the act as well, delivering a powerful free-kick which the over-worked Foster again did well to keep out and substitute Brahim Diaz and Bernardo Silva almost scored from yet another counter.
Aguero completed the scoring in the final minute with an impressive chip over Foster after Sterling had played him into the Albion area with a selfless pass.
Ederson 6; Walker 7, Otamendi 6, Laporte 6, Zinchenko 7; Fernandinho 7; B. Silva 7, De Bruyne 9 (Diaz 77, 6), D. Silva 7 (Gundogan 39, 6), Sterling 7; Aguero 6.
Foster 9; Dawson 6 , McAuley 5, Hegazy 6, Nyom 6; Field 5 (Phillips 55, 6), Krychowiak 5 (Barry 32, 6), Yacob 6, McClean 5; Rondon 5 (Sturridge 77, 5), Rodriguez 5.
R. Madley 7