Aguero went eight games without scoring for club and country, but he has found his shooting boots again after netting two, while Gundogan also scored twice in a relatively comfortable Premier League clash for Pep Guardiola's men.
Aside from Nacer Chadli's curling effort, which dropped just over the crossbar in the fourth minute, the hosts had little to shout about in an attacking sense during the first half.
Nolito had the ball in the back of the net in the early stages of the clash, but it was disallowed due to Aguero being offside when he played the pass forward for his teammate.
A few minutes later, Nolito escaped a straight red card and was issued with a yellow from referee Lee Mason instead, despite appearing to headbutt Craig Dawson after the West Brom defender clipped his heels.
City began to pile on the pressure as Sterling had a first-time volley from the edge of the box saved by Foster, while John Stones's attempt off a corner kick resulted in the ball falling wide of the target.
Any doubts that Guardiola may have had about Aguero were surely dashed when the striker broke the deadlock in the 20th minute with a thumping shot into the bottom corner of the net.
The Argentine got on the end of Gundogan's pass, which split the two defenders, and finished off the move with a confident strike past Foster.
The goalkeeper was called into action a minute later when Fernandinho struck from 30 yards out, but the Baggies shot-stopper prevented the ball from sneaking into the top corner.
Aguero continued to terrorise West Brom's defence, and he nabbed his second goal of the day by cutting to his right before drilling the ball across the keeper and into the top corner.
The hosts struggled to get out of their own half, but when they did, they failed to make their chances count as Stones comfortably cleared two crosses into the danger area in the final few minutes of the first half.
After the break, City picked up where they left off as they peppered West Brom's half with waves of attacks, but on a handful of occasions they were denied by their own teammate.
David Silva unleashed a powerful shot from the edge of the box, but Nolito got in the way by deflecting the ball wide, and a few minutes later his positioning caused more trouble.
Gundogan, who was influential in midfield, went for glory, but once again, Nolito blocked and the ball bobbled just inches from the bottom corner.
However, Salomon Rondon got there first and managed to get a header on the ball, but he missed the target and the opportunity was gone.
The home side improved as the clock ticked along, and Chadli had an opportunity to get his team back in the game with a shot from 25 yards out, but the ball went wide.
A matter of moments after coming off the bench, Kevin De Bruyne made an impact as he fizzed the ball across the face of goal to find Aguero, who repeated his effort from the back post.
Dawson got a touch on the ball, but his clearance ended up at the feet of Sterling, whose shot from 12 yards out soared over the crossbar.
The Baggies had another big chance to score when James McClean broke down the left-hand side before picking out Rondon, whose effort fell wide.
It was a better second-half display from Tony Pulis's team, but City extended their lead when Gundogan sent the ball into the back of the net after latching on to the end of Aguero's reverse pass.
Gundogan wrapped up the match by slotting home from 10 yards after being picked out by De Bruyne.
As it stands, City sit at the top of the Premier League table, level on points with Arsenal, while West Brom sit 15th, three points above relegation.