Aguero struck inside six minutes and City took a one-goal advantage into the break, before an unforgiving second half display from Roberto Mancini's side produced three further goals as West Brom offered little in the way of going forward.
Coupled with Manchester United's 1-0 defeat at Wigan, City closed the gap to their rivals and the league leaders to five points to add life to the title race, their prospects in which had appeared dead and buried before Wednesday evening's results. Whilst City remain some way off United, this victory gave them renewed hope with five games of the season still left to play.
City got off to the best possible start when Aguero gave them the lead shortly after kick-off, taking advantage of West Brom's failure to close him down. Advancing with the ball and unchallenged the Argentine unleashed a shot from the edge of the area which flew past Ben Foster and into the bottom left corner, as City began the task of adding another victim to the long list of those who have fallen to defeat at Eastlands this season.
City put the squeeze on their opponents after, running the rule in midfield with David Silva and Samir Nasri pulling the strings and Aguero causing all manner of discomfort for Roy Hodgson's side at any given opportunity.
Silva had two chances to put the ball past Foster but was unsuccessful before West Brom had a short spell of their own in which Simon Cox flashed the ball across the face of goal and Keith Andrews tried his luck from the edge of the box.
It was a brief flurry however, as Micah Richards restored the momentum in City's favour when he rounded Foster and had a shot cleared by Jonas Olsson with the goalkeeper beaten.
A goal to the good at half-time City re-emerged in the same adventurous spirit they had displayed in the opening 45 minutes, and in the 54th Aguero added his second with a neat sidefooter past Foster after being laid on wonderfully by Nasri.
It started a 10-minute goal flurry in which City scored three times, and the next name on the scoresheet was that of Tevez. Making his first start since last September as the suspended Mario Balotelli watched on from the stands, the Argentine forward arrived right on time to slot home his compatriot Aguero's cut-back from the by-line to make it 3-0.
Silva completed a bruising spell with City's fourth just three minutes later, drawing Foster from his line before lifting the ball over the West Brom keeper beautifully as City stretched their unbeaten run at home in the Premier League to 27 games, 25 of which they have now won.
There was still time for Aguero to go close to completing his hat-trick when he headed just over the bar, but it remained 4-0 as City bounced back from their defeat at Arsenal over the weekend with a resounding win.